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A290370 Number of partitions of n into distinct parts that contain primes to odd powers only (A002035). 1
1, 0, 1, 1, 0, 2, 1, 2, 3, 2, 4, 4, 3, 7, 5, 8, 9, 9, 12, 12, 14, 18, 18, 22, 27, 25, 34, 34, 39, 47, 49, 57, 67, 67, 83, 88, 96, 115, 119, 139, 154, 165, 190, 206, 224, 259, 273, 311, 341, 367, 415, 447, 490, 550, 588, 654, 720, 771, 862, 928, 1013, 1121, 1204, 1324, 1448, 1554, 1716, 1850, 2008, 2203, 2366 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

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

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(8) = 3 because we have [8], [6, 2] and [5, 3].

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[1 + Boole[And @@ OddQ /@ FactorInteger[k][[All, 2]]] x^k, {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A002035, A290369.

Sequence in context: A246833 A213624 A080845 * A029166 A096920 A087154

Adjacent sequences:  A290367 A290368 A290369 * A290371 A290372 A290373

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 28 2017

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)