A290369 Number of partitions of n into parts that contain primes to odd powers only (A002035).

1, 0, 1, 1, 1, 2, 3, 3, 5, 5, 8, 9, 12, 15, 19, 23, 29, 35, 43, 52, 64, 77, 93, 111, 134, 158, 190, 225, 266, 315, 372, 435, 514, 599, 703, 819, 955, 1110, 1290, 1493, 1732, 1998, 2309, 2659, 3062, 3518, 4040, 4630, 5305, 6063, 6931, 7907, 9015, 10265, 11680, 13268, 15070, 17087, 19366, 21923, 24799

Offset

0,6

Links

Table of n, a(n) for n=0..60.

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^A002035(k)).

Example

a(7) = 3 because we have [7], [5, 2] and [3, 2, 2].

Mathematica

nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[And @@ OddQ /@ FactorInteger[k][[All, 2]]] x^k), {k, 2, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A002035, A290370.

Sequence in context: A350865 A120249 A058690 * A087153 A240176 A134408

Adjacent sequences: A290366 A290367 A290368 * A290370 A290371 A290372

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 28 2017

Status

approved