A286320 Number of partitions of n into distinct powerful parts (A001694).

1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 4, 5, 3, 2, 4, 5, 3, 2, 4, 6, 4, 2, 4, 7, 5, 2, 5, 8, 5, 2, 5, 8, 6, 3, 5, 10, 8, 4, 6, 10, 8, 4, 6, 10, 9, 5, 8, 12, 10, 6, 9, 13, 10, 6, 9, 15, 12, 7, 10, 17, 14, 7, 11, 18, 15, 8, 11, 18, 16, 9, 11, 20, 18, 10, 13

Offset

0,10

Links

Table of n, a(n) for n=0..100.

Eric Weisstein's World of Mathematics, Powerful Number

Index entries for sequences related to powerful numbers

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} (1 + x^A001694(k)).

a(n) = A284171(n) for n < 72.

Example

a(25) = 3 because we have [25], [16, 9] and [16, 8, 1].

Mathematica

nmax = 100; CoefficientList[Series[(1 + x) Product[1 + Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001694, A284171, A286305.

Sequence in context: A334462 A054848 A284171 * A330888 A194525 A330466

Adjacent sequences: A286317 A286318 A286319 * A286321 A286322 A286323

Keyword

nonn

Author

Ilya Gutkovskiy, May 12 2017

Status

approved