A349696 Smallest number in a set of three consecutive triangular numbers each with three prime factors (counted with multiplicity).

153, 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

153 is the only known number in the sequence which is not squarefree.

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = A000217(A255200(n)). - Michel Marcus, Dec 25 2021

Example

a(1) = 153 because 153 is the smallest number in the first set of three consecutive triangular numbers with three prime factors (counted with multiplicity), i.e., (153 = 3*3*17, 171 = 3*3*19, 190 = 2*5*19).

Mathematica

t[n_] := n*(n + 1)/2; q[n_] := PrimeOmega[n] == 3; Select[Partition[t /@ Range[10^5], 3, 1], AllTrue[#, q] &][[;; , 1]] (* Amiram Eldar, Nov 25 2021 *)
(#(#+1))/2&/@SequencePosition[PrimeOmega[Accumulate[Range[170000]]], {3, 3, 3}][[;; , 1]] (* Harvey P. Dale, Oct 20 2023 *)

Crossrefs

Cf. A000217, A128896, A255200, A348185.

Sequence in context: A056733 A256748 A256741 * A246629 A371082 A325376

Adjacent sequences: A349693 A349694 A349695 * A349697 A349698 A349699

Keyword

nonn

Author

Shyam Sunder Gupta, Nov 25 2021

Extensions

Definition clarified by Harvey P. Dale, Oct 20 2023

Status

approved