A286221 Number of partitions of n into distinct parts with an even number of distinct prime divisors.

1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 6, 5, 5, 6, 7, 9, 10, 10, 12, 11, 11, 15, 16, 15, 17, 18, 19, 23, 26, 25, 27, 30, 33, 37, 38, 39, 46, 50, 52, 57, 59, 61, 71, 77, 78, 84, 91, 97, 107, 114, 120, 131, 139, 147, 163, 172, 180, 197

Offset: 0

Author

Ilya Gutkovskiy, May 04 2017

Keywords

• nonn

Examples

			a(21) = 4 because we have [21], [20, 1], [15, 6] and [14, 6, 1].
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Distinct Prime Factors
• Index entries for related partition-counting sequences

Crossrefs

Cf. A030231, A285798, A286220.

Programs

Mathematica

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

Formula

G.f.: Product_{k>=1} (1 + x^A030231(k)).