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A259677
Octagonal numbers (A000567) that are semiprimes (A001358).
3
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
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
KEYWORD
nonn
AUTHOR
Colin Barker, Jul 03 2015
STATUS
approved