OFFSET
1,1
COMMENTS
153 is the only known number in the sequence which is not squarefree.
FORMULA
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