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%I #15 Jan 09 2024 00:02:54
%S 1,1,2,5,7,2,11,13,15,16,19,10,11,4,14,29,32,33,9,19,5,41,5,47,49,52,
%T 55,28,59,60,65,67,69,71,75,19,13,20,7,85,88,89,46,95,97,98,103,7,36,
%U 22,113,57,59,15,31,63,8,129,133,67,68,139,145,49,25,151,154,156,159,8,33
%N Numerator of bigomega(n!)/omega(n!).
%C a(n) is the numerator of A022559(n)/A000720(n). - _Robert Israel_, Jan 08 2024
%H Robert Israel, <a href="/A088531/b088531.txt">Table of n, a(n) for n = 2..10000</a>
%F Let B = number of prime divisors of n! with multiplicity, O = number of distinct prime divisors of n! Then a(n) = numerator of B/O.
%e a(4!) = bigomega(4!) / omega(4!) = 4/2 = 2
%p N:= 100:
%p W:= ListTools:-PartialSums(map(numtheory:-bigomega,[$1..N])):
%p seq(numer(W[i]/numtheory:-pi(i)),i=2..N); # _Robert Israel_, Jan 08 2024
%t Table[Numerator[PrimeOmega[n!]/PrimeNu[n!]],{n,2,80}] (* _Harvey P. Dale_, Jan 17 2015 *)
%o (PARI) for(x=2,100,x1=x!;y=bigomega(x1)/omega(x1);print1(numerator(y)", "))
%Y Cf. A000720, A022559.
%K nonn,look
%O 2,3
%A _Cino Hilliard_, Nov 16 2003
%E Edited by _T. D. Noe_, Apr 14 2009
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