cp's OEIS Frontend

A087183 Partition numbers of the form 3*k.

%I A087183 #36 May 22 2025 06:53:44
%S A087183 3,15,30,42,135,231,297,627,792,1002,1575,2436,5604,8349,10143,14883,
%T A087183 31185,37338,44583,63261,105558,147273,239943,281589,329931,614154,
%U A087183 1121505,1505499,3087735,4087968,4697205,8118264,15796476,44108109
%N A087183 Partition numbers of the form 3*k.
%C A087183 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 is known that there are infinitely many partition numbers divisible by 2. - _Jonathan Vos Post_, Jul 31 2008
%C A087183 Intersection of A008585 and A000041. - _Reinhard Zumkeller_, Nov 03 2009
%D A087183 Erica Klarreich, Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes, Science News, Jun 18 2005.
%H A087183 Paul Tek, <a href="/A087183/b087183.txt">Table of n, a(n) for n = 1..10000</a>
%H A087183 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 A087183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunction.html">Partition Function</a>.
%H A087183 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%F A087183 A079978(a(n))*A167392(a(n)) = 1. - _Reinhard Zumkeller_, Nov 03 2009
%F A087183 a(n) = 3*A213365(n). - _Omar E. Pol_, May 08 2013
%F A087183 a(n) = A000041(A083214(n)). - _Amiram Eldar_, May 22 2025
%t A087183 Select[PartitionsP@Range[120], Divisible[#, 3] &] (* _Vladimir Reshetnikov_, Nov 05 2015 *)
%o A087183 (PARI) for(n=9, 1e3, t=numbpart(n); if(t%3, , print1(t", "))) \\ _Charles R Greathouse IV_, May 08 2013
%Y A087183 Cf. A000041, A008585, A068907, A052001, A052003, A079978, A083214, A087180, A087184, A087185, A167392, A213365.
%K A087183 nonn
%O A087183 1,1
%A A087183 _Reinhard Zumkeller_, Aug 23 2003