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%I #27 Feb 08 2022 08:05:54
%S 3,15,30,42,135,231,297,627,792,1002,1575,2436,5604,8349,10143,14883,
%T 31185,37338,44583,63261,105558,147273,239943,281589,329931,614154,
%U 1121505,1505499,3087735,4087968,4697205,8118264,15796476,44108109
%N Partition numbers of the form 3*k.
%C The numbers m such that 3 divides A000041(m) are given in A083214. Klarreich writes: no one has proved whether there are infinitely many partition numbers divisible by 3, although it's known that there are infinitely many partition numbers divisible by 2. - _Jonathan Vos Post_, Jul 31 2008
%C Intersection of A008585 and A000041; A079978(a(n))*A167392(a(n)) = 1. - _Reinhard Zumkeller_, Nov 03 2009
%D Erica Klarreich, Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes, Science News, Jun 18 2005.
%H Paul Tek, <a href="/A087183/b087183.txt">Table of n, a(n) for n = 1..10000</a>
%H Erica Klarreich, <a href="https://www.thefreelibrary.com/Pieces+of+numbers%3A+a+proof+brings+closure+to+a+dramatic+tale+of...-a0134386252">Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes</a>, Science News, Jun 18 2005.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunction.html">Partition Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>
%F a(n) = 3*A213365(n). - _Omar E. Pol_, May 08 2013
%t Select[PartitionsP@Range[120], Divisible[#, 3] &] (* _Vladimir Reshetnikov_, Nov 05 2015 *)
%o (PARI) for(n=9, 1e3, t=numbpart(n); if(t%3, , print1(t", "))) \\ _Charles R Greathouse IV_, May 08 2013
%Y Cf. A000041, A087180, A087184, A087185, A068907, A052001, A052003, A083214.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 23 2003
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