A280596 Expansion of Product_{p prime, k>=2} (1 + x^(p^k)).

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, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 3, 3, 1, 1, 3, 3, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 3, 1, 4, 4, 3, 1, 4, 5, 3, 2, 4, 6, 3, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 6, 4, 2, 4, 7, 4, 2, 4, 7, 5, 2

Offset: 0

Author

Ilya Gutkovskiy, Jan 06 2017

Keywords

• nonn

Comments

Number of partitions of n into distinct proper prime powers (A246547).

Examples

			a(25) = 2 because we have [25] and [16, 9].
		

Links

• Eric Weisstein's World of Mathematics, Prime Power
• Index entries for related partition-counting sequences

Crossrefs

Cf. A054685, A106244, A246547, A280586.

Programs

Mathematica

nmax = 107; CoefficientList[Series[Product[(1 + Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k), {k, 2, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{p prime, k>=2} (1 + x^(p^k)).