A113302 - OEIS

%I #5 Mar 30 2012 17:22:41

%S 0,1,0,1,0,0,2,2,0,0,0,0,4,2,3,0,0,0,0,0,6,0,0,0,0,0,0,2,2,2,0,2,0,0,

%T 0,0,0,0,0,2,2,0,3,4,0,2,0,0,0,0,6,0,0,0,0,0,2,0,2,2,2,2,2,2,0,0,0,0,

%U 2,0,0,0,0,2,0,3,0,0,4,2,2,4,0,0,3,2,0,2,0,0,2,0,0,0,0,6,2,2,0,0,2,0,4,2,0

%N Number of k such that prime(n) divides T(k), the central trinomial coefficient A002426(k), with 0<k<prime(n).

%C For primes less than 10^6, a(n) <= 10. Is 10 the largest possible value? When a(n)=0, prime(n) is in A113305. When a(n)>0, prime(n) is in A113304.

%H T. D. Noe, <a href="/A113302/b113302.txt">Table of n, a(n) for n=1..1000</a>

%t nn=1000; a=b=1; t=Join[{1}, Table[c=((2n-1)b+3(n-1)a)/n; a=b; b=c; c, {n, 2, nn}]]; Table[p=Prime[i]; cnt=0; Do[If[Mod[t[[j]], p]==0, cnt++ ], {j, p}]; cnt, {i, PrimePi[nn]}]

%Y Cf. A113303 (least k such that prime(n) divides T(k)).

%K nonn

%O 1,7

%A _T. D. Noe_, Oct 24 2005