A380007 Hexagonal numbers that are sphenic numbers.

66, 190, 231, 435, 561, 861, 946, 1653, 2278, 3655, 4371, 5151, 5995, 6441, 8911, 9453, 10011, 10585, 13366, 15051, 15753, 16471, 20301, 21115, 22366, 22791, 23653, 26335, 32131, 33153, 39621, 40186, 45451, 50403, 54946, 62481, 69751, 72771, 77421, 80601, 83845, 93961, 99235, 102831

Offset: 1

Author

Massimo Kofler, Jan 08 2025

Keywords

• nonn

Examples

			66 = 2*3*11 is the product of 3 distinct primes and the 6th hexagonal number hex(6) = 6*(2*6-1).
231 = 3*7*11 is the product of 3 distinct primes and the 11th hexagonal number hex(11) = 11*(2*11-1).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000384 and A007304.

Cf. A129521.

Programs

Mathematica

semiQ[k_] := FactorInteger[k][[;; , 2]] == {1, 1}; q[k_] := (PrimeQ[k] && semiQ[2*k - 1]) || (PrimeQ[2*k - 1] && semiQ[k]); Table[k*(2*k - 1), {k, Select[Range[250], q]}] (* Amiram Eldar, Jan 08 2025 *)