A290370 Number of partitions of n into distinct parts that contain primes to odd powers only (A002035).

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

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