%I A022559
%S A022559 0,0,1,2,4,5,7,8,11,13,15,16,19,20,22,24,28,29,32,33,36,38,40,41,45,
%T A022559 47,49,52,55,56,59,60,65,67,69,71,75,76,78,80,84,85,88,89,92,95,97,
%U A022559 98,103,105,108,110,113,114,118,120,124,126,128,129,133,134,136,139
%N A022559 Sum of exponents in prime-power factorization of n!.
%H A022559 Daniel Forgues, <a href="b022559.txt">Table of n, a(n) for n=0..100000</
               a>
%H A022559 K. Matthews, <a href="http://www.numbertheory.org/php/factorial.html">
               Computing the prime-power factorization of n!</a>
%p A022559 with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(numbperm(n)) 
               fi end: seq(a(n), n=0..63); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 11 2008
%t A022559 Array[Plus@@Last/@FactorInteger[ #! ]&,5!,0] [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Nov 10 2009]
%o A022559 (PARI) v=[]; for(n=1,200,v=concat(v,bigomega(n!))); v
%Y A022559 a(n) = a(n-1)+A001222(n).
%Y A022559 A027746(a(A000040(n))+1) = A000040(n), A082288(a(n)+1) = n.
%Y A022559 Cf. A001221(n!) = omega(n!) = pi(n) = A000720(n).
%Y A022559 Adjacent sequences: A022556 A022557 A022558 this_sequence A022560 A022561 
               A022562
%K A022559 nonn
%O A022559 0,4
%A A022559 Karen E. Wandel (kw29(AT)evansville.edu)
%E A022559 Typo corrected by Daniel Forgues (squid(AT)zensearch.com), Nov 16 2009