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Tetrahedral (or triangular pyramidal) numbers which are products of three distinct primes (or sphenic numbers).
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%I #8 Aug 06 2022 08:29:58

%S 165,286,455,969,1771,4495,9139,12341,32509,176851,437989,657359,

%T 939929,3737581,9290431,21084251,26536591,39338069,44101441,61690919,

%U 92568571,112805879,289442201,381588019,439918931,495593039,711215371,815946449,1008077071,1103914379

%N Tetrahedral (or triangular pyramidal) numbers which are products of three distinct primes (or sphenic numbers).

%C A squarefree subsequence of tetrahedral numbers a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.

%e 165 = 9*10*11/6 = 3*5*11

%e 286 = 11*12*13/6 = 2*11*13

%e 455 = 13*14*15/6 = 5*7*13

%e 9139 = 37*38*39/6 = 13*19*37

%t Select[Table[n*(n + 1)*(n + 2)/6, {n, 1, 2000}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* _Amiram Eldar_, Jul 26 2022 *)

%Y Intersection of A000292 and A007304.

%Y Subsequence of A070755.

%K nonn

%O 1,1

%A _Massimo Kofler_, Jul 26 2022