A285798 Number of partitions of n into parts with an even number of distinct prime divisors.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 5, 5, 6, 7, 8, 8, 11, 11, 14, 16, 19, 19, 25, 26, 31, 34, 40, 41, 51, 53, 62, 68, 80, 85, 103, 107, 124, 135, 157, 166, 195, 205, 235, 256, 294, 311, 362, 383, 437, 472, 535, 568, 652, 695, 786, 847, 954, 1016, 1155, 1231, 1381, 1486, 1662, 1774, 1997, 2130, 2377, 2557, 2846

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for related partition-counting sequences

Formula

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

Example

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

Mathematica

nmax = 70; CoefficientList[Series[Product[1/(1 - Boole[EvenQ[PrimeNu[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A030231, A087153 (number of partitions into parts with an even number of divisors), A285799.

Sequence in context: A029193 A308052 A005858 * A321346 A291444 A219795

Adjacent sequences: A285795 A285796 A285797 * A285799 A285800 A285801

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2017

Status

approved