OFFSET
0,6
COMMENTS
If n belongs to A048247 then a(n) is equal to zero.
For a given prime p and n satisfying p^k + p^(k-1) + ... + 1 <= n < p^(k+1) + ... + 1 for some k, let r_k = n mod (p^k + p^(k-1) + ... + 1), r_(k-1) = r_k mod (p^(k-1) + ... + 1), and so on down to r_1 = r_2 mod (p + 1). Then, p^n appears in a factorial m! iff none of the r_i is congruent to -1. - Charlie Neder, Nov 03 2018
LINKS
Jinyuan Wang, Table of n, a(n) for n = 0..1000
EXAMPLE
For n = 11, there are three distinct prime factors (3, 5, 11) in factorization of m!.
3^10 divides 26! ( 26! is not divisible by 3^11).
3^13 divides 27!.
5^10 divides 49! ( 49! is not divisible by 5^11).
5^12 divides 50!.
11^10 divides 120! ( 120! is not divisible by 11^11).
11^12 divides 121!.
The exponent of three distinct prime factors never becomes equal to 11. (It searches for all the exponent of prime factorization of factorials [A000142].)
Therefore a(11)=3.
PROG
(PARI) is(k, p) = my(c, s); while(s<k, c++; s+=1+valuation(c, p)); s>k;
a(n) = sum(p=2, n, isprime(p)&&is(n, p)); \\ Jinyuan Wang, Aug 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Naohiro Nomoto, Jun 08 2013
STATUS
approved