A259677 Octagonal numbers (A000567) that are semiprimes (A001358).

21, 65, 133, 341, 481, 1541, 4033, 5461, 6533, 8321, 11041, 13333, 14981, 31621, 38081, 48133, 56033, 79381, 83333, 97921, 109061, 111361, 133141, 188501, 197633, 206981, 219781, 229633, 256961, 282133, 293281, 328021, 340033, 360533, 416641, 481601, 556421

Offset

1,1

Links

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

Formula

Equals A000567 intersect A001358.

Example

The octagonal number 21 is in the sequence because 21 = 3 * 7.

Mathematica

a={}; Do[If[PrimeOmega[n (3 n - 2)]==2, AppendTo[a, n(3 n - 2)]], {n, 1, 200}]; a (* Vincenzo Librandi, Jul 04 2015 *)
Select[PolygonalNumber[8, Range[500]], PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 15 2019 *)

Prog

(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(8, n)))
(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

Crossrefs

Cf. A129521, A245365, A259676.

Sequence in context: A041866 A020211 A014641 * A089115 A259244 A020309

Adjacent sequences: A259674 A259675 A259676 * A259678 A259679 A259680

Keyword

nonn

Author

Colin Barker, Jul 03 2015

Status

approved