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Centered pentagonal numbers which are products of three distinct primes (or sphenic numbers).
0

%I #19 Oct 03 2023 15:53:28

%S 1266,1626,2806,3706,4731,6126,7426,7701,9766,10726,13506,15801,18706,

%T 19581,25251,26266,26781,31641,35106,36906,40006,50766,52926,56626,

%U 57381,62806,69306,71826,74391,76126,85101,90726,93606,95551,96531,99501,106606,108681,109726,117181,121551,123766

%N Centered pentagonal numbers which are products of three distinct primes (or sphenic numbers).

%e A005891(22) = 1266 = (5*22^2 + 5*22 + 2)/2 = 2 * 3 * 211.

%e A005891(25) = 1626 = (5*25^2 + 5*25 + 2)/2 = 2 * 3 * 271.

%e A005891(33) = 2806 = (5*33^2 + 5*33 + 2)/2 = 2 * 23 * 61.

%t Select[Table[5*n*(n + 1)/2 + 1, {n, 0, 225}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* _Amiram Eldar_, Sep 07 2023 *)

%Y Intersection of A005891 and A007304.

%K nonn

%O 1,1

%A _Massimo Kofler_, Sep 07 2023