A349696 - OEIS

%I #18 Oct 20 2023 18:37:46

%S 153,406,861,39621,2166321,3924201,11146281,14804961,19198306,

%T 73951041,83417986,97951006,209643526,310415986,522339681,526225461,

%U 583333246,611153241,801460666,1601581906,2520251506,2690954841,4455349606,6681853401,9895642221,13878029901

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

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

%F a(n) = A000217(A255200(n)). - _Michel Marcus_, Dec 25 2021

%e 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).

%t 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 *)

%t (#(#+1))/2&/@SequencePosition[PrimeOmega[Accumulate[Range[170000]]],{3,3,3}][[;;,1]] (* _Harvey P. Dale_, Oct 20 2023 *)

%Y Cf. A000217, A128896, A255200, A348185.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Nov 25 2021

%E Definition clarified by _Harvey P. Dale_, Oct 20 2023