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A008476 If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

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

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 *)

PROG

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

CROSSREFS

Sequence in context: A126241 A019777 A090885 * A300657 A112621 A081448

Adjacent sequences:  A008473 A008474 A008475 * A008477 A008478 A008479

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

More terms from Benoit Cloitre, Jun 07 2002

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)