cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A062274 #33 Jul 29 2023 06:37:34
%S A062274 0,0,1,7,45,291,2030,15695,135045,1287243,13495669,154516663,
%T A062274 1919455487,25721712601,369942275033
%N A062274 Number of prime divisors (with repetition) of (n!)!, A000197.
%F A062274 a(n) = A001222(A000197(n)). - _Michel Marcus_, Oct 20 2019
%t A062274 Table[PrimeOmega[(n!)!],{n,0,10}] (* _Harvey P. Dale_, Apr 29 2015 *)
%o A062274 (PARI) for(n=0, 10, print1(bigomega(n!!), ", "))
%o A062274 (PARI)  a(n) = { my(res = 0, nf = n!); forprime(p = 2, nf, res+=val(nf, p) ); res }
%o A062274 val(n, p) = my(r=0); while(n, r+=n\=p);r \\ _David A. Corneth_, Apr 10 2021
%o A062274 (Python)
%o A062274 from sympy import factorial,factorint
%o A062274 def A062274(n): return sum(sum(factorint(i).values()) for i in range(2,factorial(n)+1)) # _Chai Wah Wu_, Apr 10 2021
%Y A062274 Cf. A000197, A001222, A003604, A022559.
%K A062274 nonn,more
%O A062274 0,4
%A A062274 _Jason Earls_, Jul 04 2001
%E A062274 More terms from _David W. Wilson_, Jul 06 2001
%E A062274 a(11)-a(13) from _Jinyuan Wang_, Apr 01 2020
%E A062274 a(14) from _David A. Corneth_, Apr 10 2021