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%I #18 Sep 08 2022 08:46:13
%S 21,65,133,341,481,1541,4033,5461,6533,8321,11041,13333,14981,31621,
%T 38081,48133,56033,79381,83333,97921,109061,111361,133141,188501,
%U 197633,206981,219781,229633,256961,282133,293281,328021,340033,360533,416641,481601,556421
%N Octagonal numbers (A000567) that are semiprimes (A001358).
%H Colin Barker, <a href="/A259677/b259677.txt">Table of n, a(n) for n = 1..1000</a>
%F Equals A000567 intersect A001358.
%e The octagonal number 21 is in the sequence because 21 = 3 * 7.
%t a={}; Do[If[PrimeOmega[n (3 n - 2)]==2, AppendTo[a, n(3 n - 2)]], {n, 1, 200}]; a (* _Vincenzo Librandi_, Jul 04 2015 *)
%t Select[PolygonalNumber[8,Range[500]],PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 15 2019 *)
%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(8, n)))
%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..500] | IsSemiprime(s) where s is n*(3*n-2) ]; // _Vincenzo Librandi_, Jul 04 2015
%Y Cf. A129521, A245365, A259676.
%K nonn
%O 1,1
%A _Colin Barker_, Jul 03 2015
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