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A259194
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Number of partitions of n into four primes.
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19
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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
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0,12
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LINKS
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FORMULA
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a(n) = [x^n y^4] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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