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

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

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