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

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, 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, 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

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Programs

Maple

A008476 := proc(n) local e,j; e := ifactors(n)[2]:
add (e[j][2]^e[j][1], j=1..nops(e)) end:
seq (A008476(n), n=1..80);
# Peter Luschny, Jan 17 2011

Mathematica

Prepend[ Array[ Plus @@ Map[ Power @@ RotateLeft[ #1, 1 ]&, FactorInteger[ # ] ]&, 100, 2 ], 1 ]
Total[ #2^#1 & @@@ FactorInteger[ # ]] & /@ Range[100] (* Peter Pein (petsie(AT)dordos.net), Dec 21 2007 *)

PARI

for(n=1, 110, print1(sum(i=1, omega(n), component(component(factor(n), 2), i)^component(component(factor(n), 1), i)), ", "))

Formula

Additive with a(p^e) = e^p.

Extensions

More terms from Benoit Cloitre, Jun 07 2002