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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 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
Intersection of A008585 and A000041; A079978(a(n))*A167392(a(n)) = 1. - 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
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
Sequence in context: A053519 A039666 A020493 * A297851 A298088 A290325
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 23 2003
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)