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A113903 Sum of omega(n!) and bigomega(n!).

%I A113903 #21 Nov 25 2024 01:28:15
%S A113903 0,0,2,4,6,8,10,12,15,17,19,21,24,26,28,30,34,36,39,41,44,46,48,50,54,
%T A113903 56,58,61,64,66,69,71,76,78,80,82,86,88,90,92,96,98,101,103,106,109,
%U A113903 111,113,118,120,123,125,128,130,134,136,140,142,144,146,150,152,154,157
%N A113903 Sum of omega(n!) and bigomega(n!).
%H A113903 Robert Israel, <a href="/A113903/b113903.txt">Table of n, a(n) for n = 0..10000</a>
%F A113903 a(n) = A000720(n) + A022559(n). - _Michel Marcus_, Nov 22 2024
%p A113903 p:= 0: w:= 0: R:= 0:
%p A113903 for n from 1 to 100 do
%p A113903   if isprime(n) then p:= p+1 fi;
%p A113903   w:= w+numtheory:-bigomega(n);
%p A113903   R:= R, p+w
%p A113903 od:
%p A113903 R; # _Robert Israel_, Nov 21 2024
%t A113903 Join[{0}, Accumulate[Array[Boole[PrimeQ[#]] + PrimeOmega[#] &, 100]]] (* _Paolo Xausa_, Nov 22 2024 *)
%o A113903 (PARI) a(n) = omega(n!) + bigomega(n!);
%Y A113903 Cf. A000142, A001221, A001222.
%Y A113903 Cf. A000720, A022559.
%Y A113903 Partial sums of A378309 (for n >= 1).
%K A113903 easy,nonn
%O A113903 0,3
%A A113903 _Cino Hilliard_, Jan 29 2006