A282569 Number of compositions (ordered partitions) of n into multiplicatively perfect numbers (A007422).

1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 10, 13, 17, 22, 31, 44, 63, 88, 122, 166, 227, 312, 433, 601, 836, 1159, 1604, 2214, 3056, 4220, 5837, 8079, 11188, 15486, 21424, 29624, 40961, 56641, 78344, 108379, 149940, 207427, 286933, 396880, 548943, 759273, 1050234, 1452740, 2009545, 2779745, 3845085, 5318633, 7356839

Offset: 0

Author

Ilya Gutkovskiy, Feb 18 2017

Keywords

• nonn

Examples

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

Links

• Eric Weisstein's World of Mathematics, Multiplicative Perfect Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A007422, A236473.

Programs

Mathematica

nmax = 52; CoefficientList[Series[1/(1 - Sum[Boole[Sqrt[k]^DivisorSigma[0, k]/k == k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

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