#include <bits/stdc++.h>

template<unsigned long maxsize, unsigned long MOD, unsigned long primesize>
class divisor_convolution_coefficients{
    unsigned long sieve[maxsize];
public:
    unsigned long prime[primesize];
    unsigned long coef[maxsize];
    constexpr divisor_convolution_coefficients() : coef(), sieve(), prime(){
        coef[1] = 1;
        for(unsigned long i = 2; i < maxsize; ++i){
            coef[i] = i;
            sieve[i] = 1;
        }
        for(unsigned long i = 2, c = 0; i < maxsize; ++i)if(sieve[i]){
            prime[c++] = i;
            for(unsigned long j = i; j < maxsize; j += i){
                sieve[j] = 0;
                (coef[j] *= MOD + 1 - i) %= MOD;
            }
        }
    }
};

constexpr unsigned long MOD = 998244353;
constexpr unsigned long mx = 1000001;
constexpr divisor_convolution_coefficients<mx, MOD, 78498> coef{divisor_convolution_coefficients<mx, MOD, 78498>()};

namespace fast {
    // fast I/O by rsk0315 (update: 2019-08-08 07:02:47).
    // This version supports only integer inputs/outputs, single character
    // outputs, and string literal outputs.
    static size_t constexpr buf_size = 1 << 17;
    static size_t constexpr margin = 1;
    static char inbuf[buf_size + margin] = {};
    static char outbuf[buf_size + margin] = {};
    static __attribute__((aligned(8))) char minibuf[32];
    static size_t constexpr int_digits = 20;  // 18446744073709551615
    static uintmax_t constexpr digit_mask = 0x3030303030303030;
    static uintmax_t constexpr first_mask = 0x00FF00FF00FF00FF;
    static uintmax_t constexpr second_mask = 0x0000FFFF0000FFFF;
    static uintmax_t constexpr third_mask = 0x00000000FFFFFFFF;
    static uintmax_t constexpr tenpow[] = {
            1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000
    };
    template <typename Tp>
    using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;

    class scanner {
        char* pos = inbuf;
        char* endpos = inbuf + buf_size;

        void M_read_from_stdin() {
            endpos = inbuf + fread(pos, 1, buf_size, stdin);
        }
        void M_reread_from_stdin() {
            ptrdiff_t len = endpos - pos;
            if (!(inbuf + len <= pos)) return;
            memcpy(inbuf, pos, len);
            char* tmp = inbuf + len;
            endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
            *endpos = 0;
            pos = inbuf;
        }

    public:
        scanner() { M_read_from_stdin(); }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_parallel(Integral& x) {
            // See https://qiita.com/rsk0315_h4x/items/17a9cb12e0de5fd918f4
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool ends = false;
            typename std::make_unsigned<Integral>::type y = 0;
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            do {
                memcpy(minibuf, pos, 8);
                long c = *(long*)minibuf;
                long d = (c & digit_mask) ^ digit_mask;
                int skip = 8;
                int shift = 8;
                if (d) {
                    int ctz = __builtin_ctzl(d);
                    if (ctz == 4) break;
                    c &= (1L << (ctz-5)) - 1;
                    int discarded = (68-ctz) / 8;
                    shift -= discarded;
                    c <<= discarded * 8;
                    skip -= discarded;
                    ends = true;
                }
                c |= digit_mask;
                c ^= digit_mask;
                c = ((c >> 8) + c*10) & first_mask;
                c = ((c >> 16) + c*100) & second_mask;
                c = ((c >> 32) + c*10000) & third_mask;
                y = y*tenpow[shift] + c;
                pos += skip;
            } while (!ends);
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_serial(Integral& x) {
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            typename std::make_unsigned<Integral>::type y = *pos-'0';
            while (*++pos >= '0') y = 10*y + *pos-'0';
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        // Use scan_parallel(x) only when x may be too large (about 10^12).
        // Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
        void scan(Integral& x) { scan_serial(x); }
    };

    class printer {
        char* pos = outbuf;

        void M_flush_stdout() {
            fwrite(outbuf, 1, pos-outbuf, stdout);
            pos = outbuf;
        }

    public:
        printer() = default;
        ~printer() { M_flush_stdout(); }

        void print(char c) {
            if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
            *pos++ = c;
        }

        template <size_t N>
        void print(char const(&s)[N]) {
            if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
            memcpy(pos, s, N-1);
            pos += N-1;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void print(Integral x) {
            if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
                M_flush_stdout();
            if (x == 0) {
                *pos++ = '0';
                return;
            }
            if (x < 0) {
                *pos++ = '-';
                if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
                    switch (sizeof x) {
                        case 2: print("32768"); return;
                        case 4: print("2147483648"); return;
                        case 8: print("9223372036854775808"); return;
                    }
                }
                x = -x;
            }
            char* mp = minibuf + sizeof minibuf;
            *--mp = x % 10 + '0';
            size_t len = 1;
            typename std::make_unsigned<Integral>::type y = x / 10;
            while (y > 0) {
                *--mp = y % 10 + '0';
                y /= 10;
                ++len;
            }
            memcpy(pos, mp, len);
            pos += len;
        }

        template <typename Tp>
        void println(Tp x) { print(x), print('\n'); }
    };
} // fast::

fast::scanner in;
fast::printer out;

int main(){
    using namespace std;

    unsigned long N;
    in.scan(N);

    unsigned long ans{0};
    vector<unsigned long> hoge(mx);
    for(unsigned long _ = 0, i; _ < N; ++_){
        in.scan(i);
        ++hoge[i];
    }

    for(const auto& i : coef.prime)for(unsigned long j = mx / i; j; --j)hoge[j] += hoge[j * i] * i;
    for(auto& i : hoge)i %= MOD;

    ans = MOD - hoge[1];
    for(unsigned long i = 1; i < mx; ++i)if(hoge[i])ans += hoge[i] * hoge[i] % MOD * coef.coef[i] % MOD;
    (ans += (ans & 1) * MOD) >>= 1;
    out.println(ans % MOD);

    return 0;
}

Measured memory_bytes: 8192