A112021 Number of partitions of n into Chen primes.
0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 30, 35, 40, 46, 52, 60, 67, 77, 87, 98, 111, 124, 140, 157, 175, 197, 219, 244, 272, 302, 336, 372, 412, 456, 503, 556, 613, 675, 742, 816, 896, 983, 1078, 1180, 1291, 1411, 1542, 1683, 1836, 2001, 2178
Offset: 1
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
fQ[n_] := PrimeQ@n && (PrimeQ[n + 2] || 2 == Plus @@ Last /@ FactorInteger[n + 2]); f[n_] := Block[{c = k = 0, l = PartitionsP@n, p = Union /@ IntegerPartitions@n}, While[k++; k < l, If[Union[fQ /@ p[[k]]] == {True}, c++ ]]; c]; lst = {}; Do[ AppendTo[lst, f[n]], {n, 61}]; lst (* or *) Rest@ CoefficientList[ Series[1/Times @@ (1 - x^Select[ Range@100, fQ@# &]), {x, 0, 61}], x] (* Robert G. Wilson v, Jun 16 2006 *) -
PARI
ok(n)={isprime(n) && bigomega(n+2)<3} {my(n=80); Vec(prod(k=1, n, if(ok(k), 1/(1-x^k) + O(x*x^n), 1))-1,-n)} \\ Andrew Howroyd, Dec 28 2017
Formula
G.f.: Product_{k>=1} 1/(1 - x^A109611(k)). - Andrew Howroyd, Dec 28 2017
Comments