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%I #8 Mar 17 2017 00:46:50
%S 1,1,0,0,0,0,1,1,1,1,1,1,0,0,2,3,2,1,1,1,1,3,4,3,3,3,2,3,4,5,5,4,5,6,
%T 5,7,9,8,7,8,9,10,11,12,12,12,13,14,16,18,18,18,17,18,22,24,26,28,27,
%U 27,29,32,36,38,38,40,42,43,46,50,54,57,60,61,62,67,71,74,79,83,88,90,94,102,106,108
%N Number of partitions of n into distinct multiplicatively perfect numbers (A007422).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePerfectNumber.html">Multiplicative Perfect Number</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^A007422(k)).
%e a(15) = 3 because we have [15], [14, 1] and [8, 6, 1].
%t nmax = 85; CoefficientList[Series[Product[1 + Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}], {x, 0, nmax}], x]
%o (PARI) a(k) = k==1 || numdiv(k) == 4;
%o Vec(prod(k=1, 85, 1 + a(k)*x^k) + O(x^86)) \\ _Indranil Ghosh_ and modified by _Michel Marcus_, Mar 17 2017
%Y Cf. A007422, A236473.
%K nonn
%O 0,15
%A _Ilya Gutkovskiy_, Mar 16 2017
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