A112022 Number of partitions of n into distinct Chen primes.

1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 6, 5, 6, 7, 6, 9, 7, 9, 9, 9, 11, 11, 11, 13, 12, 14, 15, 14, 17, 15, 17, 19, 18, 21, 21, 21, 24, 24, 26, 28, 27, 30, 30, 32, 35, 34, 37, 37, 39, 41, 43, 45, 46, 48, 51, 53, 56, 58, 59, 61, 64, 66, 70, 71, 73

Offset

0,6

Comments

a(n) = A000586(n) for n <= 42.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Formula

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

Mathematica

terms = 81;
gf = Times @@ (1 + x^SequencePosition[ PrimeOmega[ Range[terms]], {1, _, 1|2}][[All, 1]]) + O[x]^terms;
CoefficientList[gf, x] (* Jean-François Alcover, Jul 02 2018 *)

Prog

(PARI) P=1+O(x^1001); forprime(p=2, 1e3, if(bigomega(p+2)<3, P*=1+x^p)); Vec(P) \\ Charles R Greathouse IV, May 13 2013

Crossrefs

Cf. A112021, A112020, A109611.

Sequence in context: A223893 A358009 A358010 * A358011 A000586 A029399

Adjacent sequences: A112019 A112020 A112021 * A112023 A112024 A112025

Keyword

nonn

Author

Reinhard Zumkeller, Aug 26 2005

Status

approved