This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A117962 #9 Jan 30 2014 17:20:27
%S A117962 6,21,66,157,388,713,1274,1977,3012,4665,6556,9257,12578,16233,20604,
%T A117962 26169,33072,40453,49364,59375,69960,82363,96058,111811,130532,150833,
%U A117962 171948,194739,218392,243817,275948,310139,347540,386043,430296,475747
%N A117962 Partial sums of hexagonal numbers with prime indices.
%C A117962 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.
%H A117962 Harvey P. Dale, <a href="/A117962/b117962.txt">Table of n, a(n) for n = 1..1000</a>
%F A117962 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)).
%e A117962 a(4) = hexagonal(2) + hexagonal(3) + hexagonal(5) + hexagonal(7) = 6 + 15 + 45 + 91 = 157 is prime.
%e A117962 a(12) = 6 + 15 + 45 + 91 + 231 + 325 + 561 + 703 + 1035 + 1653 + 1891 + 2701 = 9257 is prime.
%e A117962 a(26) = 150833 is prime.
%t A117962 Accumulate[Table[n(2n-1),{n,Prime[Range[50]]}]] (* _Harvey P. Dale_, Jan 30 2014 *)
%Y A117962 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.
%Y A117962 Cf. A000005, A000040, A000384, A001021, A034953, A001248, A116995, A117961, A117965.
%K A117962 easy,nonn,less
%O A117962 1,1
%A A117962 _Jonathan Vos Post_, Apr 05 2006