Problem:


Score : 400 points

Problem Statement

For a positive integer X, let f(X) be the number of positive divisors of X.

Given a positive integer N, find \sum_{K=1}^N K\times f(K).

Constraints

1 \leq N \leq 10^7

Input

Input is given from Standard Input in the following format:

N

Output

Print the value \sum_{K=1}^N K\times f(K).

Sample Input 1

4

Sample Output 1

23

We have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is 1\times 1 + 2\times 2 + 3\times 2 + 4\times 3 =23.

Sample Input 2

100

Sample Output 2

26879

Sample Input 3

10000000

Sample Output 3

838627288460105

Watch out for overflows.



Sample input:
4


Sample output:
23

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = modfactorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') # 26
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            # 配列の値を葉にセット
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            # 構築していく
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    # ************ Graph ************
    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 最短経路問題: https://ja.wikipedia.org/wiki/%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E5%95%8F%E9%A1%8C
    
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    # Warshall Floyd O(V**3)
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        # ref: https://juppy.hatenablog.com/entry/2018/11/01/%E8%9F%BB%E6%9C%AC_python_%E5%85%A8%E7%82%B9%E5%AF%BE%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E6%B3%95%EF%BC%88%E3%83%AF%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%95%E3%83%AD%E3%82%A4%E3%83%89%E6%B3%95
        # number_vertex: len(vertex)
        # XYD: list of distance from x to y
        # shift_one_for_vertex: XYDの値が1~Nの時(0~N-1でない時)に調整するフラグ。
        # d[i][j]: iからjへの最短距離
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 # distance of same vertex is 0
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%

    N = r_int()
    l = [0] * N
    for i in range(1, N+1):
        j = 1
        while i * j <= N:
            l[i*j-1] += 1
            j += 1
    ans = 0
    for i, ll in enumerate(l, 1):
        ans += i * ll
    print(ans)


    # D = r_int()
    # C = R()
    # S = [R() for _ in range(D)]
    # # T = [r_int() for _ in range(D)]
    
    # def calc_score(D, C, S, T):
    #     sat = 0
    #     satl = [0] * D
    #     DI = [0] * 26 # daily irritation
    #     T_ = [t-1 for t in T]
    #     for i, t in enumerate(T_):
    #         for j in range(26):
    #             if j != t:
    #                 DI[j] += 1
    #                 sat -= C[j] * DI[j]
    #             else: # j == t
    #                 DI[j] = 0
    #                 sat += S[i][j]
    #         satl[i] = sat
    #     # return satl
    #     return sat
    
    # def donyoku(D, C, S):
    #     # return T
    #     DI = [0] * 26
    #     T = [0] * D
    #     for i in range(D):
    #         candidate = -1
    #         candidate_value = -INF
    #         for j in range(26):
    #             tmp_j = (DI[j] + 1) * C[j] + S[i][j] # merit
    #             if candidate_value < tmp_j:
    #                 candidate_value = tmp_j
    #                 candidate = j
    #         T[i] = candidate
    #     return [t+1 for t in T]

    # def emphasize_c(D, C, S, emp = 0.9):
    #     # return T
    #     DI = [0] * 26
    #     T = [0] * D
    #     for i in range(D):
    #         candidate = -1
    #         candidate_value = -INF
    #         for j in range(26):
    #             tmp_j = (DI[j] + 1) * C[j] + S[i][j] * emp # merit
    #             if candidate_value < tmp_j:
    #                 candidate_value = tmp_j
    #                 candidate = j
    #         T[i] = candidate
    #     return [t+1 for t in T]

    # def update_one(T, score):
    #     target_t = random.randint(0, D-1)
    #     after_abc = random.randint(1, 24)
    #     before_abc = T[target_t]
    #     T[target_t] = after_abc
    #     tmp = calc_score(D, C, S, T)
    #     if score < tmp:
    #         score = tmp
    #     else:
    #         T[target_t] = before_abc
    #     return T, score
    
    # def change_two(T, score):
    #     target_1, target_2 = random.sample(range(0, D), 2)
    #     before_1 = T[target_1]
    #     before_2 = T[target_2]
    #     T[target_1] = before_2
    #     T[target_2] = before_1
    #     tmp = calc_score(D, C, S, T)
    #     if score < tmp:
    #         score = tmp
    #     else:
    #         T[target_1] = before_1
    #         T[target_2] = before_2
    #     return T, score

    # import time
    # start = time.perf_counter()
    
    # T = [1] * D
    # score = -INF
    # Cand = [donyoku(D, C, S), emphasize_c(D, C, S), emphasize_c(D, C, S, 0.5), emphasize_c(D, C, S, 0)]
    # for c in Cand:
    #     tmp = calc_score(D, C, S, c)
    #     if tmp > score:
    #         T = c
    #         score = tmp
    
    # import random
    # while time.perf_counter() - start < 1.8:
    #     if random.random() < 0.5:
    #         T, score = update_one(T, score)
    #     else:
    #         T, score = change_two(T, score)

    # print(*T, sep='\n')


    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n = int(input())

ans = 0
for i in range(1, int(n ** 0.5) + 1):
    cnt = ((n // i) * (n // i + 1) // 2) - (i * (i + 1) // 2)
    ans += i * cnt * 2 + i ** 2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())

ans = 0
for i in range(1,n+1):
    num = n//i
    ans += num*(i+i*num)//2

print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N = int(input())
Answer = 0

for i in range(1,N+1):
    cnt = N // i
    num = cnt * (cnt + 1) >> 1
    num *= i
    Answer += num

print(Answer)

Submission status: Accepted

Solution code:
N = int(input())
print(sum(i*(N//i)*(N//i + 1) // 2 for i in range(1,N+1) ))

Submission status: Accepted

Solution code:

N = int(input())

Answer = 0

for i in range(1,N+1):
    num = i*(N//i)*(N//i + 1) // 2
    Answer += num

print(Answer)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
#S,L,R = map(int, input().split())

N = int(input())

Answer = 0

for i in range(1,N+1):
    num = (N//i)*(N//i + 1) // 2
    num *= i
    Answer += num

print(Answer)

Submission status: Accepted

Solution code:
from numba import njit
@njit('void(i8)')
def f(N):
  Answer = 0
  for i in range(1,N+1):
    num = (N//i)*(N//i + 1) // 2
    num *= i
    Answer += num
  print(Answer)

f(int(input()))

Submission status: Accepted

Solution code:
import sys
import math
from collections import deque
input = sys.stdin.readline
#S,L,R = map(int, input().split())

N = int(input())

Answer = 0

for i in range(1,N+1):
    num = (N//i)*(N//i + 1) // 2
    num *= i
    Answer += num

print(Answer)

Submission status: Accepted

Solution code:
N = int(input())
ans = 0
for i in range(1, N+1):
    y = N//i
    ans += i*y*(y+1)//2
print(ans)

Submission status: Accepted

Solution code:
def main():
    n = int(input())

    sum = 0
    for j in range(n):
        j += 1
        # for i in range(n):
        #     if i % j == 0:
        #         sum += i
        k = n // j
        sum += (k * (1 + k) // 2) * j

    print(sum)


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
n = int(input())

ans = 0
for i in range(1, n+1):
  y = n//i
  ans += i * y * (y+1) // 2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())

r = 0
for d in range(1, N+1):
	Y = N//d
	r += d * Y * (Y+1)//2
print(r)

Submission status: Accepted

Solution code:
n = int(input())
ans = 0
for i in range(1, n+1):
    y = n // i
    ans +=( y * (y+1)* i)//2

print(ans)

Submission status: Accepted

Solution code:
import sys
#DEBUG=True
DEBUG=False
if DEBUG:
    f=open("202006_5th/D_input.txt")
else:
    f=sys.stdin
ans_sum=0
n=int(f.readline().strip())
for _ in range(1,n+1):
    num=n//_
    ans_sum+=_*((num*(num+1))//2)
print(ans_sum)

Submission status: Accepted

Solution code:
import math
n=int(input())
ans=0
for i in range(1,n+1):
  ans+=(i+(n//i)*i)*(n//i)//2
print(ans)

Submission status: Accepted

Solution code:
from sys import stdin
input = lambda: stdin.readline().rstrip("\r\n")
from collections import defaultdict as vector, deque as que
read = lambda: list(map(int,input().split()))
from bisect import bisect
from heapq import heappush as hpush,heappop as hpop

n,=read()
ans=0
for i in range(1,n+1):
	c=n//i 
	k=(c*(c+1))//2
	ans+=i*k 
print(ans)

Submission status: Accepted

Solution code:
N = int(input())

ans = 0
for i in range(1, N+1):
    tmp = i*(N//i)
    ans += (N//i)*(tmp+i)//2
print(ans)

Submission status: Accepted

Solution code:
N = int(input())

t = 0

for i in range (1,N+1):
  p = N//i
  t += i*p*(1+p)/2
  

print(int(t))

Submission status: Accepted

Solution code:
n = int(input())
res = 0
for i in range(1,n+1):
	k = n//i
	res += i*(k*(k+1)//2)
print(res)

Submission status: Accepted

Solution code:
import sys
from io import StringIO
import unittest
import os

sys.setrecursionlimit(999999999)

def get_arithmetic_progression(a, d, n):
    return n * (2 * a + (n - 1) * d) // 2

# 実装を行う関数
def resolve(test_def_name=""):
    n = int(input())

    ans = 0
    for i in range(1, n + 1):
        ans += get_arithmetic_progression(i, i, n // i)

    print(ans)


# テストクラス
class TestClass(unittest.TestCase):
    def assertIO(self, assert_input, output):
        stdout, sat_in = sys.stdout, sys.stdin
        sys.stdout, sys.stdin = StringIO(), StringIO(assert_input)
        resolve(sys._getframe().f_back.f_code.co_name)
        sys.stdout.seek(0)
        out = sys.stdout.read()[:-1]
        sys.stdout, sys.stdin = stdout, sat_in
        self.assertEqual(out, output)

    def test_input_1(self):
        test_input = """4"""
        output = """23"""
        self.assertIO(test_input, output)

    def test_input_2(self):
        test_input = """100"""
        output = """26879"""
        self.assertIO(test_input, output)

    # def test_input_3(self):
    #     test_input = """10000000"""
    #     output = """838627288460105"""
    #     self.assertIO(test_input, output)

    # 自作テストパターンのひな形(利用時は「tes_t」のアンダーバーを削除すること
    def tes_t_1original_1(self):
        test_input = """データ"""
        output = """データ"""
        self.assertIO(test_input, output)


# 実装orテストの呼び出し
if __name__ == "__main__":
    if os.environ.get("USERNAME") is None:
        # AtCoder提出時の場合
        resolve()

    else:
        # 自PCの場合
        unittest.main()

Submission status: Accepted

Solution code:
num = int(input())
val = 0
for i in range(1,num+1):
  k = num//i
  val += i*(k*(k+1))//2
print(val)

Submission status: Accepted

Solution code:
n = int(input())
ans = 0

for i in range(1, n + 1):
    ans += (i + (n//i)*i)*(n//i)//2

print(ans)

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
import math
from bisect import bisect_left
from bisect import bisect_right
from collections import defaultdict
from heapq import heappop, heappush
import itertools
import random
from decimal import *

input = sys.stdin.readline

def inputInt(): return int(input())
def inputMap(): return map(int, input().split())
def inputList(): return list(map(int, input().split()))
def inputStr(): return input()[:-1]

inf = float('inf')
mod = 1000000007

#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-

def main():
	N = inputInt()

	ans = 0
	total = N * (N+1) // 2
	for i in range(1,N+1):
		tmp = i * ((N//i) * ((N//i)+1) // 2)
		ans += tmp

	print(ans)



#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
if __name__ == "__main__":
	main()

Submission status: Accepted

Solution code:
# -*- coding: utf-8 -*-
import sys
import math
from bisect import bisect_left
from bisect import bisect_right
from collections import defaultdict
from heapq import heappop, heappush
import itertools
import random
from decimal import *

input = sys.stdin.readline

def inputInt(): return int(input())
def inputMap(): return map(int, input().split())
def inputList(): return list(map(int, input().split()))
def inputStr(): return input()[:-1]

inf = float('inf')
mod = 1000000007

#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-

def main():
	N = inputInt()
	Nnum = [0 for i in range(N+1)]

	for i in range(1,N+1):
		for j in range(i,N+1,i):
			Nnum[j] += 1

	ans = 0
	for i,val in enumerate(Nnum):
		ans += i * val

	print(ans)



#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
#-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
if __name__ == "__main__":
	main()

Submission status: Accepted

Solution code:
def calc(i):
    cnt = n // i
    return (i + i*cnt) * cnt // 2

n = int(input())

ans = 0
for i in range(1, n+1):
    ans += calc(i)

print(ans)

Submission status: Accepted

Solution code:
import bisect, collections, copy, heapq, itertools, math, string, sys
input = lambda: sys.stdin.readline().rstrip() 
sys.setrecursionlimit(10**7)
INF = float('inf')
def I(): return int(input())
def F(): return float(input())
def SS(): return input()
def LI(): return [int(x) for x in input().split()]
def LI_(): return [int(x)-1 for x in input().split()]
def LF(): return [float(x) for x in input().split()]
def LSS(): return input().split()

def resolve():
    N = I()

    ans = 0
    for i in range(1, N + 1):
        num = N // i
        e = num * i
        ans += (i + e) * num // 2

    print(ans)

if __name__ == '__main__':
    resolve()

Submission status: Accepted

Solution code:
n = int(input())

ans = 0
for i in range(1, n + 1):
  A = i
  D = i
  N = n // i
  ans += N * (2 * A + (N - 1) * D) // 2

print(ans)

Submission status: Accepted

Solution code:
N=int(input())
ans = 0
for i in range(1,N+1):
  p = N//i
  ans+=(2*i+(p-1)*i)*p//2
print(ans)

Submission status: Accepted

Solution code:
N=int(input())
ans = 0
for i in range(1,N+1):
  p = N//i
  ans+=i*(1+p)*p//2
print(ans)

Submission status: Accepted

Solution code:
n = int(input())


def f(x):
    return x * (x + 1) // 2


ans = 0
for x in range(1, n + 1):
    if x * x > n:
        break
    ans += x * x
    y_high = n // x
    ans += 2 * x * (f(y_high) - f(x))
print(ans)

Submission status: Accepted

Solution code:
n = int(input())
ret = 0
for i in range(1, n+1):
    cnt = n // i
    tt = cnt * (cnt+1) * i // 2
    ret += tt
print(ret)