

A259194


Number of partitions of n into four primes.


19



0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 2, 3, 3, 4, 4, 6, 3, 6, 5, 7, 5, 9, 5, 11, 7, 11, 7, 13, 6, 14, 9, 15, 8, 18, 9, 21, 10, 19, 11, 24, 10, 26, 12, 26, 13, 30, 12, 34, 15, 33, 16, 38, 14, 41, 17, 41, 16, 45, 16, 50, 19, 47, 21, 56, 20, 61, 20, 57
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OFFSET

0,12


LINKS



FORMULA

a(n) = [x^n y^4] Product_{k>=1} 1/(1  y*x^prime(k)).  Ilya Gutkovskiy, Apr 18 2019


EXAMPLE

a(17) = 3 because 17 can be written as the sum of four primes in exactly three ways: 2+2+2+11, 2+3+5+7 and 2+5+5+5.


MATHEMATICA

a[n_] := Length@ IntegerPartitions[n, {4}, Prime@ Range@ PrimePi@ n]; a /@
Table[Count[IntegerPartitions[n, {4}], _?(AllTrue[#, PrimeQ]&)], {n, 0, 80}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2019 *)


PROG

(PARI) a(n) = {nb = 0; forpart(p=n, if (#p && (#select(x>isprime(x), Vec(p)) == #p), nb+=1), , [4, 4]); nb; } \\ Michel Marcus, Jun 21 2015
(Magma) [0] cat [#RestrictedPartitions(n, 4, {d:d in PrimesUpTo(n)}):n in [1..100]]; // Marius A. Burtea, May 07 2019


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



