A062274 Number of prime divisors (with repetition) of (n!)!, A000197.

0, 0, 1, 7, 45, 291, 2030, 15695, 135045, 1287243, 13495669, 154516663, 1919455487, 25721712601, 369942275033

Offset: 0

Author

Jason Earls, Jul 04 2001

Keywords

• nonn
• more

Crossrefs

Cf. A000197, A001222, A003604, A022559.

Programs

Mathematica

Table[PrimeOmega[(n!)!],{n,0,10}] (* Harvey P. Dale, Apr 29 2015 *)

PARI

for(n=0, 10, print1(bigomega(n!!), ", "))

PARI

a(n) = { my(res = 0, nf = n!); forprime(p = 2, nf, res+=val(nf, p) ); res }
val(n, p) = my(r=0); while(n, r+=n\=p);r \\ David A. Corneth, Apr 10 2021

Python

from sympy import factorial,factorint
def A062274(n): return sum(sum(factorint(i).values()) for i in range(2,factorial(n)+1)) # Chai Wah Wu, Apr 10 2021

Formula

a(n) = A001222(A000197(n)). - Michel Marcus, Oct 20 2019

Extensions

More terms from David W. Wilson, Jul 06 2001

a(11)-a(13) from Jinyuan Wang, Apr 01 2020

a(14) from David A. Corneth, Apr 10 2021