A122964 Semiprimes with triangular indices.

4, 9, 15, 26, 39, 58, 85, 111, 134, 166, 205, 237, 291, 327, 382, 445, 497, 545, 623, 697, 766, 841, 921, 1003, 1114, 1195, 1285, 1379, 1486, 1622, 1718, 1837, 1943, 2071, 2195, 2329, 2483, 2605, 2787, 2935, 3073, 3214, 3379, 3554, 3742, 3909, 4105, 4286

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = semiprime(T(1)), where T(n) is the n-th triangular number. a(n) = A001358(A000217(n)) = A001358(n*(n+1)/2).

Example

a(1) = semiprime(T(1)) = semiprime(1) = 4 = 2^2.
a(2) = semiprime(T(2)) = semiprime(3) = 9 = 3^2.
a(3) = semiprime(T(3)) = semiprime(6) = 15 = 3 * 5.
a(4) = semiprime(T(4)) = semiprime(10) = 26 = 2 * 13.

Mathematica

Module[{nn=3000, sem, tr, len}, sem=Select[Range[nn], PrimeOmega[#]==2&]; len = Length[sem]; tr=Table[If[OddQ[Sqrt[8n+1]], 1, 0], {n, len}]; Pick[ sem, tr, 1]](* Harvey P. Dale, Apr 24 2018 *)

Crossrefs

Cf. A000217, A001358.

Sequence in context: A364013 A056928 A225283 * A301254 A291318 A178379

Adjacent sequences: A122961 A122962 A122963 * A122965 A122966 A122967

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 27 2006

Extensions

a(24)-a(48) from Giovanni Resta, Jun 13 2016

Status

approved