A284171 - OEIS

A284171

Number of partitions of n into distinct perfect powers (including 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, 7, 11, 10, 6, 8, 12, 10, 6, 8, 13, 11, 7, 9, 15, 13, 7, 10, 16, 14, 8, 10, 16, 15, 9, 10, 17, 16, 9, 11

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OFFSET

0,10

COMMENTS

Differs from the sequence A112345 which does not consider 1 as a perfect power.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Perfect Power

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} (1 + x^A001597(k)).

a(n) = A112345(n-1) + A112345(n).