

A285799


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


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for related partitioncounting 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]


CROSSREFS

Cf. A001156 (number of partitions into parts with an odd number of divisors), A030230, A285798.
Sequence in context: A093950 A280715 A023894 * A241772 A323053 A059777
Adjacent sequences: A285796 A285797 A285798 * A285800 A285801 A285802


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Apr 26 2017


STATUS

approved



