A352166 Number of partitions of n into distinct odd prime powers (1 included).

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 4, 5, 6, 6, 6, 7, 8, 9, 9, 10, 12, 12, 13, 14, 16, 17, 17, 19, 21, 23, 23, 25, 28, 30, 31, 33, 37, 38, 40, 43, 47, 50, 52, 55, 60, 64, 66, 70, 76, 81, 83, 89, 96, 101, 105, 110, 119, 125, 130, 138, 147, 155, 161

Offset

0,9

Links

Table of n, a(n) for n=0..70.

Formula

G.f.: Product_{k>=0} (1 + x^A061345(k)).

Mathematica

nmax = 70; CoefficientList[Series[Product[(1 + Boole[(PrimePowerQ[k] || k == 1) && OddQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A024939, A054685, A061345, A106244, A134337, A280152, A352165.

Sequence in context: A091226 A097913 A029269 * A272187 A194621 A088004

Adjacent sequences: A352163 A352164 A352165 * A352167 A352168 A352169

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 06 2022

Status

approved