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A286320 Number of partitions of n into distinct powerful parts (A001694). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 15:47 EDT 2022. Contains 355994 sequences. (Running on oeis4.)