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

0,16

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A030231, A285798, A286220.

Sequence in context: A333123 A289494 A029286 * A321347 A324383 A342789

Adjacent sequences: A286218 A286219 A286220 * A286222 A286223 A286224

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved