A117961 Hexagonal numbers with prime indices.

6, 15, 45, 91, 231, 325, 561, 703, 1035, 1653, 1891, 2701, 3321, 3655, 4371, 5565, 6903, 7381, 8911, 10011, 10585, 12403, 13695, 15753, 18721, 20301, 21115, 22791, 23653, 25425, 32131, 34191, 37401, 38503, 44253, 45451, 49141, 52975, 55611

Offset: 1

Author

Jonathan Vos Post, Apr 05 2006

Keywords

• easy
• nonn
• less

Comments

See also: A034953 Triangular numbers (A000217) with prime indices. A001248 Squares of primes. A116995 Pentagonal numbers with prime indices. A000384 Hexagonal numbers: n(2n-1). There are no prime hexagonal numbers. The n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.

Crossrefs

Cf. A000005, A000040, A000384, A001021, A034953, A001248, A116995.

Programs

Mathematica

With[{hex=Table[n(2n-1),{n,250}]},Flatten[Table[Take[hex,{Prime[n]}],{n, 40}]]] (* Harvey P. Dale, Dec 04 2011 *)

Formula

a(n) = A000040(n)*(2*A000040(n)-1). a(n) = A000384(prime(n)). a(n) = number of divisors of 12^(prime(n)-1) = A000005(A001021(A000040(n)-1)).