cp's OEIS Frontend

A052284 Number of compositions of n into nonprime numbers.

%I A052284 #26 Aug 06 2019 17:37:46
%S A052284 1,1,1,1,2,3,5,7,11,17,27,40,61,92,142,217,333,506,774,1181,1807,2758,
%T A052284 4215,6434,9833,15019,22948,35047,53541,81780,124936,190841,291532,
%U A052284 445320,680274,1039155,1587405,2424849,3704148,5658321,8643530
%N A052284 Number of compositions of n into nonprime numbers.
%C A052284 Starting at n=1, appears to be row sums of triangle A157424. - _Gary W. Adamson_ & _Mats Granvik_, Feb 28 2009
%H A052284 Alois P. Heinz, <a href="/A052284/b052284.txt">Table of n, a(n) for n = 0..5437</a> (first 501 terms from T. D. Noe)
%F A052284 G.f.: 1/( 1 - (Sum_{m nonprime} x^m) ).
%e A052284 a(6) = 5 because 1+1+1+1+1+1 = 1+1+4 = 1+4+1 = 4+1+1 = 6.
%p A052284 a:= proc(n) option remember; `if`(n=0, 1, add(
%p A052284       `if`(isprime(j), 0, a(n-j)), j=1..n))
%p A052284     end:
%p A052284 seq(a(n), n=0..45);  # _Alois P. Heinz_, Aug 06 2019
%t A052284 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 *)
%Y A052284 Cf. A002095 (Number of partitions of n into nonprime parts).
%Y A052284 Cf. A000041 & A023360.
%Y A052284 Column k=0 of A224344.
%K A052284 nonn
%O A052284 0,5
%A A052284 _Robert G. Wilson v_, May 16 2002
%E A052284 Definition and g.f. corrected by _N. J. A. Sloane_, Aug 19 2010, who thanks _Vladimir Kruchinin_ for pointing out the errors.