A259676 Heptagonal numbers (A000566) that are semiprimes (A001358).

34, 55, 235, 403, 469, 697, 1177, 1651, 2059, 2839, 4141, 5221, 6943, 9211, 9517, 13213, 13579, 21949, 23377, 25351, 29539, 31753, 34633, 37027, 53071, 62173, 68641, 74563, 78943, 93799, 96727, 118483, 130759, 144841, 164737, 171217, 187279, 191407, 196981

Offset: 1

Author

Colin Barker, Jul 03 2015

Keywords

• nonn

Comments

For these semiprimes k*(5*k-3)/2, the corresponding k are listed in A114517.

Examples

			The heptagonal number 34 is in the sequence because 34 = 2 * 17.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A129521, A245365, A259677.

Programs

Magma

IsSemiprime:=func; [s: n in [2..300] | IsSemiprime(s) where s is n*(5*n-3) div 2]; // Vincenzo Librandi, Jul 04 2015

Mathematica

a={}; Do[If[PrimeOmega[n (5 n - 3) / 2]==2, AppendTo[a, n(5 n - 3) / 2]], {n, 1, 200}]; a (* Vincenzo Librandi, Jul 04 2015 *)
Select[PolygonalNumber[7,Range[300]],PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 07 2021 *)

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
select(n->bigomega(n)==2, vector(2000, n, pg(7, n)))

Formula

Equals A000566 intersect A001358.