%I A135369
%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 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)
%F A135369 a(n) = A008474(n!) if n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 28 2008
%p A135369 A001222 := proc(n) numtheory[bigomega](n) ; end: A008472 := proc(n) add(op(1,
               i),i=ifactors(n)[2]) ; end: A008474 := proc(n) A001222(n)+A008472(n) 
               ; end: A135369 := proc(n) if n < 2 then n+1 ; else A008474(n!) ; 
               fi ; end: seq(A135369(n),n=0..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Feb 28 2008
%Y A135369 Cf. A000142.
%Y A135369 Sequence in context: A096072 A014837 A019312 this_sequence A109660 A075855 
               A140189
%Y A135369 Adjacent sequences: A135366 A135367 A135368 this_sequence A135370 A135371 
               A135372
%K A135369 easy,nonn
%O A135369 0,2
%A A135369 Ctibor O. ZIZKA (ctibor.zizka(AT)seznam.cz), Feb 17 2008
%E A135369 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 28 2008