A286222 Number of partitions of n into distinct parts with an odd number of prime divisors (counted with multiplicity).

1, 0, 1, 1, 0, 2, 0, 2, 2, 1, 3, 2, 3, 4, 3, 5, 4, 5, 7, 6, 10, 8, 10, 12, 10, 15, 14, 16, 20, 18, 25, 25, 28, 32, 31, 38, 38, 44, 49, 51, 59, 61, 68, 75, 79, 89, 93, 103, 113, 120, 137, 141, 157, 168, 176, 200, 205, 229, 245, 260, 289, 303, 332, 356, 376, 411, 433, 470, 507, 535, 587

Offset

0,6

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^A026424(k)).

Example

a(10) = 3 because we have [8, 2], [7, 3] and [5, 3, 2].

Mathematica

nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026424, A286218, A286220, A286223.

Sequence in context: A003823 A059451 A083817 * A029273 A117963 A321594

Adjacent sequences: A286219 A286220 A286221 * A286223 A286224 A286225

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved