A097796 - OEIS

%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