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%I #24 Sep 14 2023 18:07:04
%S 1,3,3,5,5,7,7,3,5,11,11,13,13,7,5,17,17,19,19,7,11,23,23,5,13,13,7,
%T 29,29,31,31,11,17,17,7,37,37,19,13,41,41,43,43,11,23,47,47,7,7,17,17,
%U 53,53,11,11,19,29,59,59,61,61,31,7,13,13,67
%N Largest prime factor of n(n+1)/2, the n-th triangular number.
%C Essentially the same as A074399, which has many comments, references and links.
%F a(n) = A006530(A000217(n)).
%e A000217(9) = 9*(9+1)/2 = 45 = 3*3*5, therefore a(9) = 5.
%t PrimeFactors[n_]:=Flatten[Table[ #[[1]],{1}]&/@FactorInteger[n]]; Table[PrimeFactors[n*(n-1)/2][[ -1]],{n,2,6!}] (* _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009 *)
%t (* Second program: *)
%t Array[FactorInteger[PolygonalNumber[#]][[-1, 1]] &, 66] (* _Michael De Vlieger_, Sep 14 2023 *)
%o (PARI) \\ written for a(n), n >= 2
%o a(n)=vecmax(factor(n*(n+1)/2)[,1]) \\ _M. F. Hasler_, May 02 2015
%Y Related properties of triangular numbers: A069901, A069903, A069904.
%Y Cf. A000217, A006530, A074399.
%K nonn,easy
%O 1,2
%A _Reinhard Zumkeller_, Apr 10 2002
%E Edited by _Peter Munn_, Sep 14 2023
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