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A349696
Smallest number in a set of three consecutive triangular numbers each with three prime factors (counted with multiplicity).
1
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.
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
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 25 2021
EXTENSIONS
Definition clarified by Harvey P. Dale, Oct 20 2023
STATUS
approved