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 A259194 Number of partitions of n into four primes. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Giovanni Resta, Table of n, a(n) for n = 0..5000 FORMULA a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(n-i-j-k). - Wesley Ivan Hurt, Apr 17 2019 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 /@ Range[0, 100] (* Giovanni Resta, Jun 21 2015 *) 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)  cat [#RestrictedPartitions(n, 4, {d:d in PrimesUpTo(n)}):n in [1..100]]; // Marius A. Burtea, May 07 2019 CROSSREFS Column k=4 of A117278. Number of partitions of n into r primes for r = 1..10: A010051, A061358, A068307, this sequence, A259195, A259196, A259197, A259198, A259200, A259201. Cf. A000040. Sequence in context: A078705 A346018 A050331 * A194344 A128435 A220415 Adjacent sequences:  A259191 A259192 A259193 * A259195 A259196 A259197 KEYWORD nonn,easy AUTHOR Doug Bell, Jun 20 2015 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)