A117962 Partial sums of hexagonal numbers with prime indices.

6, 21, 66, 157, 388, 713, 1274, 1977, 3012, 4665, 6556, 9257, 12578, 16233, 20604, 26169, 33072, 40453, 49364, 59375, 69960, 82363, 96058, 111811, 130532, 150833, 171948, 194739, 218392, 243817, 275948, 310139, 347540, 386043, 430296, 475747

Offset

1,1

Comments

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = SUM[i=1..n] A117961(i). a(n) = SUM[i=1..n] A000040(i)*(2*A000040(i)-1). a(n) = SUM[i=1..n] A000384(prime(n)). a(n) = Partial sum of number of divisors of 12^(prime(n)-1) = SUM[i=1..n] A000005(A001021(A000040(n)-1)).

Example

a(4) = hexagonal(2) + hexagonal(3) + hexagonal(5) + hexagonal(7) = 6 + 15 + 45 + 91 = 157 is prime.
a(12) = 6 + 15 + 45 + 91 + 231 + 325 + 561 + 703 + 1035 + 1653 + 1891 + 2701 = 9257 is prime.
a(26) = 150833 is prime.

Mathematica

Accumulate[Table[n(2n-1), {n, Prime[Range[50]]}]] (* Harvey P. Dale, Jan 30 2014 *)

Crossrefs

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). A117961 Hexagonal numbers with prime indices. A117965 Prime partial sums of hexagonal numbers with prime indices.

Cf. A000005, A000040, A000384, A001021, A034953, A001248, A116995, A117961, A117965.

Sequence in context: A228704 A320855 A319613 * A105457 A134931 A119103

Adjacent sequences: A117959 A117960 A117961 * A117963 A117964 A117965

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Apr 05 2006

Status

approved