A356422 Heptagonal numbers (or 7-gonal numbers, i.e., numbers of the form k*(5*k - 3)/2) which are products of three distinct primes (or sphenic numbers).

286, 874, 970, 1918, 3367, 3553, 4558, 6682, 8323, 8614, 11122, 11458, 12145, 14707, 16687, 17098, 17935, 18361, 19669, 21022, 27931, 30085, 33466, 38254, 42055, 42706, 44023, 44689, 46717, 48094, 50197, 55279, 61387, 64561, 73702, 79834, 81631, 82537, 85285, 88078, 89965, 92833, 101707, 105781, 108889

Offset

1,1

Comments

A squarefree subsequence of heptagonal numbers.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

286 = 2*11*13 = 11(5*11-3)/2.
1918 = 2*7*137 = 28(5*28-3)/2.
8323 = 7*29*41 = 58(5*58-3)/2.
42055 = 5*13*647 = 130(5*130-3)/2.

Mathematica

Select[Table[n*(5*n - 3)/2, {n, 1, 210}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Aug 07 2022 *)
Select[PolygonalNumber[7, Range[250]], PrimeNu[#]==PrimeOmega[#]==3&] (* Harvey P. Dale, Feb 06 2023 *)

Crossrefs

Intersection of A000566 and A007304.

Sequence in context: A025384 A256000 A253329 * A329392 A253322 A241616

Adjacent sequences: A356419 A356420 A356421 * A356423 A356424 A356425

Keyword

nonn

Author

Massimo Kofler, Aug 07 2022

Status

approved