

A087183


Partition numbers of the form 3*k.


15



3, 15, 30, 42, 135, 231, 297, 627, 792, 1002, 1575, 2436, 5604, 8349, 10143, 14883, 31185, 37338, 44583, 63261, 105558, 147273, 239943, 281589, 329931, 614154, 1121505, 1505499, 3087735, 4087968, 4697205, 8118264, 15796476, 44108109
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OFFSET

1,1


COMMENTS

The numbers n such that 3 divides A000041(n) 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
Intersection of A008585 and A000041; A079978(a(n))*A167392(a(n)) = 1. [From Reinhard Zumkeller, Nov 03 2009]


REFERENCES

Erica Klarreich, Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes, Science News, Jun 18 2005.


LINKS

Paul Tek, Table of n, a(n) for n = 1..10000
Erica Klarreich, Pieces of numbers: a proof brings closure to a dramatic tale of partitions and primes, Science News, Jun 18 2005.
Eric Weisstein's World of Mathematics, Partition Function
Eric Weisstein's World of Mathematics, Partition Function P Congruences


FORMULA

a(n) = 3*A213365(n).  Omar E. Pol, May 08 2013


MATHEMATICA

Select[PartitionsP@Range[120], Divisible[#, 3] &] (* Vladimir Reshetnikov, Nov 05 2015 *)


PROG

(PARI) for(n=9, 1e3, t=numbpart(n); if(t%3, , print1(t", "))) \\ Charles R Greathouse IV, May 08 2013


CROSSREFS

Cf. A000041, A087180, A087184, A087185, A068907, A052001, A052003, A083214.
Sequence in context: A053519 A039666 A020493 * A297851 A298088 A290325
Adjacent sequences: A087180 A087181 A087182 * A087184 A087185 A087186


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Aug 23 2003


STATUS

approved



