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 A282570 Number of ways to write n as an ordered sum of two multiplicatively perfect numbers (A007422). 1

%I

%S 0,0,1,0,0,0,0,2,0,2,0,2,1,0,2,2,5,0,2,0,3,2,4,4,2,2,0,4,5,4,3,2,4,2,

%T 4,6,8,4,0,4,6,8,5,6,5,4,2,8,10,8,2,0,7,6,7,4,8,4,2,8,10,12,2,6,4,10,

%U 9,6,9,4,7,6,14,12,2,6,5,10,7,10,8,4,4,10,14,8,6,6,10,8,10,12,15,8,6,14

%N Number of ways to write n as an ordered sum of two multiplicatively perfect numbers (A007422).

%C Conjecture: a(n) > 0 for all n > 51.

%H Ilya Gutkovskiy, <a href="/A282570/a282570.pdf">Extended graphical example</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativePerfectNumber.html">Multiplicative Perfect Number</a>

%F G.f.: (Sum_{k>=1} x^A007422(k))^2.

%e a(16) = 5 because we have [15, 1], [10, 6], [8, 8], [6, 10] and [1, 15].

%t nmax = 95; CoefficientList[Series[Sum[Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}]^2, {x, 0, nmax}], x]

%Y Cf. A007422, A236473, A280683, A282569.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Feb 18 2017

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Last modified January 20 17:05 EST 2019. Contains 319335 sequences. (Running on oeis4.)