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

Author

Reinhard Zumkeller, Sep 05 2005

Keywords

• nonn

Examples

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

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

Crossrefs

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

Formula

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

Extensions

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