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A112021 Number of partitions of n into Chen primes. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) = A000607(n) for n <= 42.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^A109611(k)). - Andrew Howroyd, Dec 28 2017

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 *)

PROG

(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

CROSSREFS

Cf. A112022, A101048, A109611.

Sequence in context: A027583 A029022 A140953 * A000607 A114372 A046676

Adjacent sequences:  A112018 A112019 A112020 * A112022 A112023 A112024

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 26 2005

STATUS

approved

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Last modified November 17 06:27 EST 2018. Contains 317275 sequences. (Running on oeis4.)