A286220 Number of partitions of n into distinct parts with an odd number of distinct prime divisors.

1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 7, 7, 10, 9, 12, 12, 15, 15, 18, 19, 22, 24, 26, 30, 32, 36, 40, 43, 49, 52, 58, 63, 69, 76, 81, 91, 96, 108, 114, 127, 135, 148, 159, 173, 186, 202, 217, 234, 253, 271, 293, 313, 339, 361, 390, 416, 449, 478, 514, 547, 588, 625, 671, 714, 763, 815, 867

Offset

0,6

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^A030230(k)).

Example

a(9) = 4 because we have [9], [7, 2], [5, 4] and [4, 3, 2].

Mathematica

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

Crossrefs

Cf. A030230, A285799, A286221.

Sequence in context: A266755 A029142 A054685 * A246581 A143619 A029141

Adjacent sequences: A286217 A286218 A286219 * A286221 A286222 A286223

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved