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A286222 Number of partitions of n into distinct parts with an odd number of prime divisors (counted with multiplicity). 3

%I #9 Aug 02 2019 13:03:06

%S 1,0,1,1,0,2,0,2,2,1,3,2,3,4,3,5,4,5,7,6,10,8,10,12,10,15,14,16,20,18,

%T 25,25,28,32,31,38,38,44,49,51,59,61,68,75,79,89,93,103,113,120,137,

%U 141,157,168,176,200,205,229,245,260,289,303,332,356,376,411,433,470,507,535,587

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

%H Amiram Eldar, <a href="/A286222/b286222.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>

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

%F G.f.: Product_{k>=1} (1 + x^A026424(k)).

%e a(10) = 3 because we have [8, 2], [7, 3] and [5, 3, 2].

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

%Y Cf. A026424, A286218, A286220, A286223.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, May 04 2017

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)