A349539 Smallest number m in a set of at least three consecutive triangular numbers with three distinct prime factors.

378, 406, 528, 820, 861, 1953, 2485, 3081, 5050, 5151, 5778, 7750, 9316, 11026, 11175, 18145, 19306, 19503, 36046, 36315, 39621, 92665, 93096, 130816, 131328, 135981, 205120, 326836, 337431, 661825, 816003, 1439056, 1993006, 1995003, 2166321, 2835771

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

a(1) = 378 because 378 is the smallest number in the first set of three consecutive triangular numbers with three distinct prime factors, i.e., (378 = 2*3^3*7, 406 = 2*7*29, 435 = 3*5*29).

Mathematica

t[n_] := n*(n + 1)/2; q[n_] := PrimeNu[n] == 3; Select[Partition[t /@ Range[3*10^3], 3, 1], AllTrue[#, q] &][[;; , 1]] (* Amiram Eldar, Nov 26 2021 *)

Crossrefs

Cf. A000217, A128896, A348185.

Sequence in context: A003918 A350183 A045197 * A098835 A134602 A268373

Adjacent sequences: A349536 A349537 A349538 * A349540 A349541 A349542

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 25 2021

Extensions

Name clarified by Michel Marcus, Dec 02 2021

Status

approved