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

Author

N. J. A. Sloane, Dec 31 2000

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A058697.

Cf. A000040, A000041, A260798.

Programs

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

Mathematica

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

Formula

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