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%I #19 Jan 08 2025 17:24:39
%S 66,190,231,435,561,861,946,1653,2278,3655,4371,5151,5995,6441,8911,
%T 9453,10011,10585,13366,15051,15753,16471,20301,21115,22366,22791,
%U 23653,26335,32131,33153,39621,40186,45451,50403,54946,62481,69751,72771,77421,80601,83845,93961,99235,102831
%N Hexagonal numbers that are sphenic numbers.
%H Amiram Eldar, <a href="/A380007/b380007.txt">Table of n, a(n) for n = 1..10000</a>
%e 66 = 2*3*11 is the product of 3 distinct primes and the 6th hexagonal number hex(6) = 6*(2*6-1).
%e 231 = 3*7*11 is the product of 3 distinct primes and the 11th hexagonal number hex(11) = 11*(2*11-1).
%t 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 *)
%Y Intersection of A000384 and A007304.
%Y Cf. A129521.
%K nonn
%O 1,1
%A _Massimo Kofler_, Jan 08 2025