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A286305
Number of partitions of n into powerful parts (A001694).
1
1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 8, 12, 14, 15, 15, 19, 21, 22, 22, 28, 33, 35, 37, 43, 48, 50, 52, 62, 70, 75, 79, 92, 100, 105, 109, 126, 140, 148, 157, 177, 194, 202, 211, 237, 261, 276, 290, 324, 351, 370, 384, 424, 462, 489, 514, 562, 609, 640, 670, 728, 787, 831, 873, 948, 1016, 1071, 1118, 1210, 1296, 1366, 1433
OFFSET
0,5
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^A001694(k)).
a(n) = A078635(n) for n < 72.
EXAMPLE
a(8) = 4 because we have [8], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 75; CoefficientList[Series[1/(1 - x) Product[1/(1 - Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 2, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 12 2017
STATUS
approved