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%I #16 Sep 13 2018 02:45:03
%S 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,
%T 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,
%U 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
%N Number of partitions of n into perfect numbers.
%C a(2*n) = A097795(n).
%C a(A204878(n)) = 0; a(A204879(n)) > 0.
%H Reinhard Zumkeller, <a href="/A097796/b097796.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectNumber.html">Perfect Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Partition.html">Partition</a>
%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Perfect_number">Perfect number</a>
%e a(90)=2: 90 = 15*6 = 15*A000396(1) = 3*28 + 1*6 = 3*A000396(2) + 1*A000396(1).
%t 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 *)
%o (Haskell)
%o a097796 = p a000396_list where
%o p _ 0 = 1
%o p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o -- _Reinhard Zumkeller_, Jan 20 2012
%Y Cf. A000396, A000041, A058696, A080225.
%K nonn
%O 1,84
%A _Reinhard Zumkeller_, Aug 25 2004
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