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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)