A058697 -id:A058697 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 31 2000

nonn

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

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

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

Cf. A058697.

Cf. A000040, A000041, A260798.

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

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

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

A247087 a(n) = pi(phi(p(P(n)))) = A000720(A000010(A000041(A000040(n)))).

Original entry on oeis.org

0, 1, 3, 4, 9, 25, 41, 39, 168, 462, 442, 1939, 2571, 3998, 5123, 17040, 24853, 38887, 195022, 183430, 404386, 381060, 1162366, 2105509, 1799881, 5966593, 5380661, 14184985, 10473967, 22631261, 135452589, 109540327, 244730051, 487610708, 604467085, 671043205, 3350187738

Offset: 1

Alois P. Heinz, Mar 14 2015

nonn

Amiram Eldar, Table of n, a(n) for n = 1..90 (calculated using Kim Walisch's primecount)
Kim Walisch, Fast C++ prime counting function implementation (primecount).

Cf. A000010, A000040, A000041, A000720, A058697, A058698, A070804.

with(numtheory): with(combinat): p:=numbpart: P:=ithprime:
a:= n-> pi(phi(p(P(n)))):
seq(a(n), n=1..20);

a[n_] := PrimePi @ EulerPhi @ PartitionsP @ Prime @ n;
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 25 2017 *)

a(n) = A070804(A058698(n)) = A000720(A000010(A000041(A000040(n)))).

a(31)-a(37) from Amiram Eldar, Sep 03 2024

cp's OEIS Frontend

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

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