A285799 - OEIS

A285799

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

%I #10 Dec 10 2020 14:52:05

%S 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,

%T 196,231,275,322,380,444,520,608,706,821,952,1102,1272,1467,1688,1941,

%U 2226,2549,2917,3329,3798,4324,4918,5587,6337,7180,8125,9184,10369,11695,13174,14828,16671,18723,21011,23551

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

%H Alois P. Heinz, <a href="/A285799/b285799.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} 1/(1 - x^A030230(k)).

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

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

%Y Cf. A001156 (number of partitions into parts with an odd number of divisors), A030230, A285798.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Apr 26 2017