A356095 Tetrahedral (or triangular pyramidal) numbers which are products of three distinct primes (or sphenic numbers).

165, 286, 455, 969, 1771, 4495, 9139, 12341, 32509, 176851, 437989, 657359, 939929, 3737581, 9290431, 21084251, 26536591, 39338069, 44101441, 61690919, 92568571, 112805879, 289442201, 381588019, 439918931, 495593039, 711215371, 815946449, 1008077071, 1103914379

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

Example

165 = 9*10*11/6 = 3*5*11
286 = 11*12*13/6 = 2*11*13
455 = 13*14*15/6 = 5*7*13
9139 = 37*38*39/6 = 13*19*37

Mathematica

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

Crossrefs

Intersection of A000292 and A007304.

Subsequence of A070755.

Sequence in context: A319328 A301970 A176877 * A323379 A215967 A029563

Adjacent sequences: A356092 A356093 A356094 * A356096 A356097 A356098

Keyword

nonn

Author

Massimo Kofler, Jul 26 2022

Status

approved