A052284 Number of compositions of n into nonprime numbers.

1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27, 40, 61, 92, 142, 217, 333, 506, 774, 1181, 1807, 2758, 4215, 6434, 9833, 15019, 22948, 35047, 53541, 81780, 124936, 190841, 291532, 445320, 680274, 1039155, 1587405, 2424849, 3704148, 5658321, 8643530

Offset: 0

Author

Robert G. Wilson v, May 16 2002

Keywords

• nonn

Comments

Starting at n=1, appears to be row sums of triangle A157424. - Gary W. Adamson & Mats Granvik, Feb 28 2009

Examples

			a(6) = 5 because 1+1+1+1+1+1 = 1+1+4 = 1+4+1 = 4+1+1 = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5437 (first 501 terms from T. D. Noe)

Crossrefs

Cf. A002095 (Number of partitions of n into nonprime parts).

Cf. A000041 & A023360.

Column k=0 of A224344.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(isprime(j), 0, a(n-j)), j=1..n))
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Aug 06 2019

Mathematica

nn=50; np=Select[Range[nn], !PrimeQ[ # ] &]; CoefficientList[Series[1/(1-Sum[x^k, {k, np}]), {x, 0, nn}], x] (* T. D. Noe, Aug 20 2010 *)

Formula

G.f.: 1/( 1 - (Sum_{m nonprime} x^m) ).

Extensions

Definition and g.f. corrected by N. J. A. Sloane, Aug 19 2010, who thanks Vladimir Kruchinin for pointing out the errors.