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A282569
Number of compositions (ordered partitions) of n into multiplicatively perfect numbers (A007422).
1
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
0,7
FORMULA
G.f.: 1/(1 - Sum_{k>=1} x^A007422(k)).
EXAMPLE
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].
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]
CROSSREFS
Sequence in context: A337567 A177332 A318155 * A372618 A213213 A319470
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 18 2017
STATUS
approved