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A290369 Number of partitions of n into parts that contain primes to odd powers only (A002035). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A099609 A120249 A058690 * A087153 A240176 A134408

Adjacent sequences:  A290366 A290367 A290368 * A290370 A290371 A290372

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 28 2017

STATUS

approved

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Last modified October 23 18:46 EDT 2018. Contains 316530 sequences. (Running on oeis4.)