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A008476
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If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j).
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2
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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; internal format)
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OFFSET
| 1,4
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FORMULA
| Additive with a(p^e) = e^p.
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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
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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
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PROG
| (PARI) for(n=1, 110, print1(sum(i=1, omega(n), component(component(factor(n), 2), i)^component(component(factor(n), 1), i)), ", "))
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CROSSREFS
| Sequence in context: A126241 A019777 A090885 * A112621 A081448 A106437
Adjacent sequences: A008473 A008474 A008475 * A008477 A008478 A008479
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 07 2002
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