Buggy python submission (verdict: Runtime Error):
import math
import sympy
n=int(input())
a=math.factorial(n)
#print(a)
#a=32400

def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors
ps=prime_factors(a)
sy={}
for i in ps:
    if i not in sy:
        sy[i]=1
    else:
        sy[i]+=1
#aaaaaaaaaaa
#sy=sympy.factorint(a)
count75=0
count25=0
count15=0
count5=0
count3=0
for k in sy.values():
    #print(k)
    if k+1>=75:
        count75+=1
    if k+1>=25:
        count25+=1
    if k+1>=15:
        count15+=1
    if k+1>=5:
        count5+=1
    if k+1>=3:
        count3+=1

#print(count75)
#print(count25*(count3-1))
#print(count15*(count5-1))
#print((count5*(count5-1)*(count3-2))/2)
print(int(count75+count25*(count3-1)+count15*(count5-1)+(count5*(count5-1)*(count3-2))/2))


Fixed submission:
import math
#import sympy
n=int(input())
a=math.factorial(n)
#print(a)
#a=32400

def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors
ps=prime_factors(a)
sy={}
for i in ps:
    if i not in sy:
        sy[i]=1
    else:
        sy[i]+=1
#aaaaaaaaaaa
#sy=sympy.factorint(a)
count75=0
count25=0
count15=0
count5=0
count3=0
for k in sy.values():
    #print(k)
    if k+1>=75:
        count75+=1
    if k+1>=25:
        count25+=1
    if k+1>=15:
        count15+=1
    if k+1>=5:
        count5+=1
    if k+1>=3:
        count3+=1

#print(count75)
#print(count25*(count3-1))
#print(count15*(count5-1))
#print((count5*(count5-1)*(count3-2))/2)
print(int(count75+count25*(count3-1)+count15*(count5-1)+(count5*(count5-1)*(count3-2))/2))

Buggy python submission (verdict: Runtime Error):
import math
import sympy
n=int(input())
a=math.factorial(n)
#print(a)
#a=32400
sy=sympy.factorint(a)
count75=0
count25=0
count15=0
count5=0
count3=0
for k in sy.values():
    #print(k)
    if k+1>=75:
        count75+=1
    if k+1>=25:
        count25+=1
    if k+1>=15:
        count15+=1
    if k+1>=5:
        count5+=1
    if k+1>=3:
        count3+=1

#print(count75)
#print(count25*(count3-1))
#print(count15*(count5-1))
#print((count5*(count5-1)*(count3-2))/2)
print(int(count75+count25*(count3-1)+count15*(count5-1)+(count5*(count5-1)*(count3-2))/2))


Fixed submission:
import math
#import sympy
n=int(input())
a=math.factorial(n)
#print(a)
#a=32400

def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors
ps=prime_factors(a)
sy={}
for i in ps:
    if i not in sy:
        sy[i]=1
    else:
        sy[i]+=1
#aaaaaaaaaaa
#sy=sympy.factorint(a)
count75=0
count25=0
count15=0
count5=0
count3=0
for k in sy.values():
    #print(k)
    if k+1>=75:
        count75+=1
    if k+1>=25:
        count25+=1
    if k+1>=15:
        count15+=1
    if k+1>=5:
        count5+=1
    if k+1>=3:
        count3+=1

#print(count75)
#print(count25*(count3-1))
#print(count15*(count5-1))
#print((count5*(count5-1)*(count3-2))/2)
print(int(count75+count25*(count3-1)+count15*(count5-1)+(count5*(count5-1)*(count3-2))/2))