

A282570


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


1



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, 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, 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
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OFFSET

0,8


COMMENTS

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


LINKS

Table of n, a(n) for n=0..95.
Ilya Gutkovskiy, Extended graphical example
Eric Weisstein's World of Mathematics, Multiplicative Perfect Number


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A007422, A236473, A280683, A282569.
Sequence in context: A243822 A277150 A156596 * A026613 A117199 A230632
Adjacent sequences: A282567 A282568 A282569 * A282571 A282572 A282573


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Feb 18 2017


STATUS

approved



