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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,84
COMMENTS
a(2*n) = A097795(n).
a(A204878(n)) = 0; a(A204879(n)) > 0.
LINKS
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
Sequence in context: A358679 A016253 A286998 * A117188 A341514 A276084
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 25 2004
STATUS
approved

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Last modified July 12 08:52 EDT 2024. Contains 374239 sequences. (Running on oeis4.)