A097796 - OEIS

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A097796

Number of partitions of n into perfect numbers.

6

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0

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OFFSET

1,84

COMMENTS

a(2*n) = A097795(n).

a(A204878(n)) = 0; a(A204879(n)) > 0.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Perfect Number

Eric Weisstein's World of Mathematics, Partition

Wikipedia, Perfect number

EXAMPLE

a(90)=2: 90 = 15*6 = 15*A000396(1) = 3*28 + 1*6 = 3*A000396(2) + 1*A000396(1).

MATHEMATICA

f[x_] := Product[-(1/(-1 + x^i)), {i, {6, 28, 496, 8128, 33550336}}]; CoefficientList[Series[f[x], {x, 0, 1000}], x] (* Ben Branman, Jan 07 2012 *)

PROG

(Haskell)

a097796 = p a000396_list where

p _ 0 = 1

p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

-- Reinhard Zumkeller, Jan 20 2012

CROSSREFS

Cf. A000396, A000041, A058696, A080225.

Sequence in context: A358679 A016253 A286998 * A117188 A341514 A276084

Adjacent sequences: A097793 A097794 A097795 * A097797 A097798 A097799

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 25 2004

STATUS

approved