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A008476 If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j).

%I A008476 #26 Jan 07 2019 02:19:38
%S A008476 0,1,1,4,1,2,1,9,8,2,1,5,1,2,2,16,1,9,1,5,2,2,1,10,32,2,27,5,1,3,1,25,
%T A008476 2,2,2,12,1,2,2,10,1,3,1,5,9,2,1,17,128,33,2,5,1,28,2,10,2,2,1,6,1,2,
%U A008476 9,36,2,3,1,5,2,3,1,17,1,2,33,5,2,3,1,17,64,2,1,6,2,2,2,10,1,10,2,5,2,2,2,26
%N A008476 If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j).
%H A008476 Vincenzo Librandi, <a href="/A008476/b008476.txt">Table of n, a(n) for n = 1..10000</a>
%F A008476 Additive with a(p^e) = e^p.
%p A008476 A008476 := proc(n) local e,j; e := ifactors(n)[2]:
%p A008476 add (e[j][2]^e[j][1], j=1..nops(e)) end:
%p A008476 seq (A008476(n), n=1..80);
%p A008476 # _Peter Luschny_, Jan 17 2011
%t A008476 Prepend[ Array[ Plus @@ Map[ Power @@ RotateLeft[ #1, 1 ]&, FactorInteger[ # ] ]&, 100, 2 ], 1 ]
%t A008476 Total[ #2^#1 & @@@ FactorInteger[ # ]] & /@ Range[100] (* Peter Pein (petsie(AT)dordos.net), Dec 21 2007 *)
%o A008476 (PARI) for(n=1, 110, print1(sum(i=1, omega(n), component(component(factor(n), 2), i)^component(component(factor(n), 1), i)), ", "))
%K A008476 nonn
%O A008476 1,4
%A A008476 _Olivier Gérard_
%E A008476 More terms from _Benoit Cloitre_, Jun 07 2002