A300584 Number of partitions of n into distinct prime power parts (not including 1) that do not divide n.

1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 4, 1, 5, 2, 4, 3, 8, 2, 11, 4, 6, 6, 18, 3, 13, 10, 10, 8, 35, 7, 42, 9, 20, 24, 22, 10, 72, 33, 35, 11, 102, 21, 120, 29, 26, 65, 161, 16, 117, 56, 93, 52, 246, 43, 113, 36, 139, 160, 370, 39, 422, 208, 102, 62, 216, 110, 613, 145, 305, 130, 780, 57, 878

Offset

0,8

Links

Table of n, a(n) for n=0..73.

Index entries for sequences related to partitions

Example

a(9) = 2 because we have [7, 2] and [5, 4].

Mathematica

Table[SeriesCoefficient[Product[(1 + Boole[Mod[n, k] != 0 && PrimePowerQ[k]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 73}]

Crossrefs

Cf. A054685, A200745, A209402, A246655, A300580.

Sequence in context: A216652 A331980 A055684 * A024559 A334664 A061797

Adjacent sequences: A300581 A300582 A300583 * A300585 A300586 A300587

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 09 2018

Status

approved