%I #26 Sep 08 2022 08:46:13
%S 34,55,235,403,469,697,1177,1651,2059,2839,4141,5221,6943,9211,9517,
%T 13213,13579,21949,23377,25351,29539,31753,34633,37027,53071,62173,
%U 68641,74563,78943,93799,96727,118483,130759,144841,164737,171217,187279,191407,196981
%N Heptagonal numbers (A000566) that are semiprimes (A001358).
%C For these semiprimes k*(5*k-3)/2, the corresponding k are listed in A114517.
%H Colin Barker, <a href="/A259676/b259676.txt">Table of n, a(n) for n = 1..1000</a>
%F Equals A000566 intersect A001358.
%e The heptagonal number 34 is in the sequence because 34 = 2 * 17.
%t 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 *)
%t Select[PolygonalNumber[7,Range[300]],PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 07 2021 *)
%o (PARI)
%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
%o select(n->bigomega(n)==2, vector(2000, n, pg(7, n)))
%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..300] | IsSemiprime(s) where s is n*(5*n-3) div 2]; // _Vincenzo Librandi_, Jul 04 2015
%Y Cf. A129521, A245365, A259677.
%K nonn
%O 1,1
%A _Colin Barker_, Jul 03 2015