A348185 Smallest number k in a set of three consecutive triangular numbers that are sphenic.

406, 861, 39621, 2166321, 3924201, 11146281, 14804961, 19198306, 73951041, 83417986, 97951006, 209643526, 310415986, 522339681, 526225461, 583333246, 611153241, 801460666, 1601581906, 2520251506, 2690954841, 4455349606, 6681853401, 9895642221, 13878029901

Offset: 1

Author

G. L. Honaker, Jr., Oct 05 2021

Keywords

• nonn

Comments

a(2)-a(9) from Chuck Gaydos.

Examples

			a(1)=406 because 406 is the smallest number in the first set of three consecutive triangular numbers that are sphenic, i.e., {406=2*7*29, 435=3*5*29, 465=3*5*31}.
		

Links

• Chris K. Caldwell and G. L. Honaker, Jr., Prime Curio for 406

Crossrefs

Cf. A000217 (triangular numbers), A007304 (sphenic numbers), A128896 (sphenic triangular numbers). Subsequence of A349696.

Programs

Mathematica

t[n_] := n*(n+1)/2; spQ[n_] := FactorInteger[n][[;;,2]] == {1,1,1}; Select[Partition[t /@ Range[170000], 3, 1], AllTrue[#, spQ] &][[;; , 1]] (* Amiram Eldar, Oct 06 2021 *)

Extensions

a(10)-a(25) from Alois P. Heinz, Oct 05 2021