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.
%I A055636 #13 Aug 14 2024 01:54:09
%S A055636 0,0,0,2,2,4,4,7,9,11,11,14,14,16,18,22,22,25,25,28,30,32,32,36,38,40,
%T A055636 43,46,46,49,49,54,56,58,60,64,64,66,68,72,72,75,75,78,81,83,83,88,90,
%U A055636 93,95,98,98,102,104,108,110,112,112,116,116,118,121,127,129,132,132
%N A055636 Partial sums of A144494.
%C A055636 Excess of prime-power exponents in n!.
%H A055636 G. C. Greubel, <a href="/A055636/b055636.txt">Table of n, a(n) for n = 1..1000</a>
%F A055636 a(n) = A046660(n!) = A046660(A000142(n)) = A022559(n) - A001221(n!) = A001222(n!) - A000720(n).
%e A055636 n=46: prime powers in factorization of 46! are {42,21,10,6,4,3,2,2,2,1,1,1,1,1}. Sum of the exponents is 97. It has 14 distinct prime divisors, so a(46)=97-14=83.
%t A055636 Table[PrimeOmega[n!] - PrimeNu[n!], {n, 1, 100}] (* _G. C. Greubel_, May 13 2017 *)
%o A055636 (PARI) for(n=1,100, print1(bigomega(n!) - omega(n!), ", ")) \\ _G. C. Greubel_, May 13 2017
%Y A055636 Cf. A046660, A000142, A022559, A001221, A001222, A000720, A144494.
%K A055636 nonn
%O A055636 1,4
%A A055636 _Labos Elemer_, Jun 07 2000
%E A055636 Simpler definition from Alan Worley (aw(AT)xiboo.co.uk), Dec 10 2008