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A062274
Number of prime divisors (with repetition) of (n!)!, A000197.
1
0, 0, 1, 7, 45, 291, 2030, 15695, 135045, 1287243, 13495669, 154516663, 1919455487, 25721712601, 369942275033
OFFSET
0,4
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
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