A058698 a(n) = p(P(n)), P = primes (A000040), p = partition numbers (A000041).

2, 3, 7, 15, 56, 101, 297, 490, 1255, 4565, 6842, 21637, 44583, 63261, 124754, 329931, 831820, 1121505, 2679689, 4697205, 6185689, 13848650, 23338469, 49995925, 133230930, 214481126, 271248950, 431149389, 541946240, 851376628, 3913864295, 5964539504, 11097645016

Offset

1,1

Comments

Number of partitions of n-th prime. - Omar E. Pol, Aug 05 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..500

Formula

a(n) = A000041(A000040(n)). - Omar E. Pol, Aug 05 2011

Example

a(2) = 3 because the second prime is 3 and there are three partitions of 3: {1, 1, 1}, {1, 2}, {3}.

Mathematica

Table[PartitionsP[Prime[n]], {n, 30}] (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)

Prog

(Haskell)
import Data.MemoCombinators (memo2, integral)
a058698 n = a058698_list !! (n-1)
a058698_list = map (pMemo 1) a000040_list where
   pMemo = memo2 integral integral p
   p _ 0 = 1
   p k m | m < k     = 0
         | otherwise = pMemo k (m - k) + pMemo (k + 1) m
-- Reinhard Zumkeller, Aug 09 2015

Crossrefs

Cf. A058697.

Cf. A000040, A000041, A260798.

Sequence in context: A216435 A110888 A133736 * A058699 A250193 A004782

Adjacent sequences: A058695 A058696 A058697 * A058699 A058700 A058701

Keyword

nonn

Author

N. J. A. Sloane, Dec 31 2000

Status

approved