A348185 - OEIS

%I #17 Jan 06 2022 15:09:16

%S 406,861,39621,2166321,3924201,11146281,14804961,19198306,73951041,

%T 83417986,97951006,209643526,310415986,522339681,526225461,583333246,

%U 611153241,801460666,1601581906,2520251506,2690954841,4455349606,6681853401,9895642221,13878029901

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

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

%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php/406.html">Prime Curio for 406</a>

%e 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}.

%t 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 *)

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

%K nonn

%O 1,1

%A _G. L. Honaker, Jr._, Oct 05 2021

%E a(10)-a(25) from _Alois P. Heinz_, Oct 05 2021