A097796 Number of partitions of n into perfect numbers.

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

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