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

1,1

Comments

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

Links

Table of n, a(n) for n=1..25.

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

Example

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}.

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 *)

Crossrefs

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

Sequence in context: A368367 A132362 A371900 * A271746 A203944 A203937

Adjacent sequences: A348182 A348183 A348184 * A348186 A348187 A348188

Keyword

nonn

Author

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

Extensions

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

Status

approved