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

0,4

Links

Table of n, a(n) for n=0..14.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000197, A001222, A003604, A022559.

Sequence in context: A099842 A287811 A115194 * A182556 A363570 A219020

Adjacent sequences: A062271 A062272 A062273 * A062275 A062276 A062277

Keyword

nonn,more

Author

Jason Earls, Jul 04 2001

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

Status

approved