A112345 Number of partitions of n into distinct perfect powers.

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 3, 3, 1, 1, 3, 4, 1, 1, 4, 4, 1, 1, 4, 4, 2, 1, 4, 6, 2, 2, 4, 6, 2, 2, 4, 6, 3, 2, 5, 6, 4, 2, 6, 6, 4, 2, 6, 7, 4, 3, 6, 9, 4, 3, 7, 9, 5, 3, 7, 9, 6, 3, 7, 10, 6, 3, 8, 11, 6, 3, 8

Offset

0,26

Links

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

Eric Weisstein's World of Mathematics, Perfect Power

Eric Weisstein's World of Mathematics, Partition

Formula

G.f.: Product_{k>=2} (1 + x^A001597(k)). - Ilya Gutkovskiy, Mar 21 2017

Example

a(40) = #{36+4, 32+8, 27+9+4} = 3.

Crossrefs

Cf. A001597, A000009, A033461, A039966, A112344, A284171.

Sequence in context: A105243 A140081 A280596 * A336469 A265262 A124763

Adjacent sequences: A112342 A112343 A112344 * A112346 A112347 A112348

Keyword

nonn

Author

Reinhard Zumkeller, Sep 05 2005

Extensions

a(0)=1 prepended by Ilya Gutkovskiy, Mar 21 2017

Status

approved