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A316154
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Number of integer partitions of prime(n) into a prime number of prime parts.
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5
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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
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OFFSET
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1,4
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LINKS
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FORMULA
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EXAMPLE
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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).
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MAPLE
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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):
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[Prime[n]], And[PrimeQ[Length[#]], And@@PrimeQ/@#]&]], {n, 20}]
(* Second program: *)
b[n_, p_, c_] := b[n, p, c] = If[n == 0 || p == 2, If[EvenQ[n] && PrimeQ[c + n/2], 1, 0], If[p>n, 0, b[n - p, p, c + 1]] + b[n, NextPrime[p, -1], c]];
a[n_] := b[Prime[n], Prime[n], 0];
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PROG
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(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
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CROSSREFS
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Cf. A000040, A000586, A000607, A038499, A056768, A064688, A070215, A085755, A302590, A316092, A316153, A316185, A344782.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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