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A348185
Smallest number k in a set of three consecutive triangular numbers that are sphenic.
2
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
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
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Oct 05 2021
EXTENSIONS
a(10)-a(25) from Alois P. Heinz, Oct 05 2021
STATUS
approved