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A135369 a(0)=1, a(1)=2; thereafter, let n! = p(1)^b(1)...p(r)^b(r) be the prime factorization of n!. Then a(n) = Sum_{i=1..r} (p(i) + b(i)).

%I A135369 #18 Mar 20 2022 18:24:14
%S A135369 1,2,3,7,9,15,17,25,28,30,32,44,47,61,63,65,69,87,90,110,113,115,117,
%T A135369 141,145,147,149,152,155,185,188,220,225,227,229,231,235,273,275,277,
%U A135369 281,323,326,370,373,376,378,426,431,433,436,438,441,495,499,501,505
%N A135369 a(0)=1, a(1)=2; thereafter, let n! = p(1)^b(1)...p(r)^b(r) be the prime factorization of n!. Then a(n) = Sum_{i=1..r} (p(i) + b(i)).
%H A135369 Harvey P. Dale, <a href="/A135369/b135369.txt">Table of n, a(n) for n = 0..1000</a>
%F A135369 a(n) = A008474(n!) if n>1. - _R. J. Mathar_, Feb 28 2008
%p A135369 A001222 := proc(n) numtheory[bigomega](n) ; end:
%p A135369 A008472 := proc(n) add(op(1,i),i=ifactors(n)[2]) ; end:
%p A135369 A008474 := proc(n) A001222(n)+A008472(n) ; end:
%p A135369 A135369 := proc(n) if n < 2 then n+1 ; else A008474(n!) ; fi ; end: seq(A135369(n),n=0..80) ; # _R. J. Mathar_, Feb 28 2008
%t A135369 Join[{1},Table[Total[Flatten[FactorInteger[n!]]],{n,60}]] (* _Harvey P. Dale_, Feb 26 2012 *)
%Y A135369 Cf. A000142, A008474.
%K A135369 easy,nonn
%O A135369 0,2
%A A135369 _Ctibor O. Zizka_, Feb 17 2008
%E A135369 More terms from _R. J. Mathar_, Feb 28 2008