A286223 Number of partitions of n into distinct parts with an even number of prime divisors (counted with multiplicity).

1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 3, 2, 0, 1, 3, 4, 4, 2, 1, 4, 6, 5, 4, 4, 6, 10, 10, 6, 6, 10, 13, 14, 11, 9, 14, 21, 21, 17, 17, 23, 31, 31, 25, 25, 33, 41, 43, 39, 38, 50, 61, 60, 56, 58, 68, 83, 87, 79, 82, 99, 115, 121, 118, 118, 139, 163, 164, 157, 165, 189, 216, 228, 221, 229, 265, 296

Offset

0,11

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Prime Factor

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} (1 + x^A028260(k)).

Example

a(10) = 3 because we have [10], [9, 1] and [6, 4].

Mathematica

nmax = 75; CoefficientList[Series[Product[1 + Boole[EvenQ[PrimeOmega[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A028260, A286219, A286221, A286222.

Sequence in context: A294201 A079618 A151844 * A341163 A329278 A348966

Adjacent sequences: A286220 A286221 A286222 * A286224 A286225 A286226

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved