A113302 Number of k such that prime(n) divides T(k), the central trinomial coefficient A002426(k), with 0

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, 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, 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

Offset: 1

Author

T. D. Noe, Oct 24 2005

Keywords

• nonn

Comments

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.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

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

Programs

Mathematica

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]}]