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A259676
Heptagonal numbers (A000566) that are semiprimes (A001358).
3
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
1,1
COMMENTS
For these semiprimes k*(5*k-3)/2, the corresponding k are listed in A114517.
LINKS
FORMULA
Equals A000566 intersect A001358.
EXAMPLE
The heptagonal number 34 is in the sequence because 34 = 2 * 17.
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 *)
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(7, n)))
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Colin Barker, Jul 03 2015
STATUS
approved