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A316154 Number of integer partitions of prime(n) into a prime number of prime parts. 2
0, 0, 1, 2, 3, 5, 9, 12, 19, 39, 50, 93, 136, 166, 239, 409, 682, 814, 1314, 1774, 2081, 3231, 4272, 6475, 11077, 14270, 16265, 20810, 23621, 30031, 68251, 85326, 118917, 132815, 226097, 251301, 342448, 463940, 565844, 759873, 1015302, 1117708, 1787452, 1961624 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from Andrew Howroyd)

FORMULA

a(n) = A085755(A000040(n)). - Alois P. Heinz, Jun 26 2018

EXAMPLE

The a(7) = 9 partitions of 17 into a prime number of prime parts: (13,2,2), (11,3,3), (7,7,3), (7,5,5), (7,3,3,2,2), (5,5,3,2,2), (5,3,3,3,3), (5,2,2,2,2,2,2), (3,3,3,2,2,2,2).

MAPLE

b:= proc(n, p, c) option remember; `if`(n=0 or p=2,

      `if`(n::even and isprime(c+n/2), 1, 0),

      `if`(p>n, 0, b(n-p, p, c+1))+b(n, prevprime(p), c))

    end:

a:= n-> b(ithprime(n)$2, 0):

seq(a(n), n=1..50);  # Alois P. Heinz, Jun 26 2018

MATHEMATICA

Table[Length[Select[IntegerPartitions[Prime[n]], And[PrimeQ[Length[#]], And@@PrimeQ/@#]&]], {n, 20}]

PROG

(PARI) seq(n)={my(p=vector(n, k, prime(k))); my(v=Vec(1/prod(k=1, n, 1 - x^p[k]*y + O(x*x^p[n])))); vector(n, k, sum(i=1, k, polcoeff(v[1+p[k]], p[i])))} \\ Andrew Howroyd, Jun 26 2018

CROSSREFS

Cf. A000040, A000586, A000607, A038499, A056768, A064688, A070215, A085755, A302590, A316092, A316153.

Sequence in context: A184794 A144728 A051147 * A079741 A000861 A108168

Adjacent sequences:  A316151 A316152 A316153 * A316155 A316156 A316157

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 25 2018

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Jun 26 2018

STATUS

approved

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Last modified April 20 14:27 EDT 2019. Contains 322310 sequences. (Running on oeis4.)