A285799 - OEIS

A285799

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

1, 0, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 15, 19, 23, 29, 37, 44, 54, 66, 80, 96, 115, 138, 165, 196, 231, 275, 322, 380, 444, 520, 608, 706, 821, 952, 1102, 1272, 1467, 1688, 1941, 2226, 2549, 2917, 3329, 3798, 4324, 4918, 5587, 6337, 7180, 8125, 9184, 10369, 11695, 13174, 14828, 16671, 18723, 21011, 23551

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OFFSET

0,5

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^A030230(k)).

EXAMPLE

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

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[OddQ[PrimeNu[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]