A069902 Largest prime factor of n(n+1)/2, the n-th triangular number.

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, 29, 29, 31, 31, 11, 17, 17, 7, 37, 37, 19, 13, 41, 41, 43, 43, 11, 23, 47, 47, 7, 7, 17, 17, 53, 53, 11, 11, 19, 29, 59, 59, 61, 61, 31, 7, 13, 13, 67

Offset: 1

Author

Reinhard Zumkeller, Apr 10 2002

Keywords

• nonn
• easy

Comments

Essentially the same as A074399, which has many comments, references and links.

Examples

			A000217(9) = 9*(9+1)/2 = 45 = 3*3*5, therefore a(9) = 5.
		

Crossrefs

Related properties of triangular numbers: A069901, A069903, A069904.

Cf. A000217, A006530, A074399.

Programs

Mathematica

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 *)
(* Second program: *)
Array[FactorInteger[PolygonalNumber[#]][[-1, 1]] &, 66] (* Michael De Vlieger, Sep 14 2023 *)

PARI

\\ written for a(n), n >= 2
a(n)=vecmax(factor(n*(n+1)/2)[,1]) \\ M. F. Hasler, May 02 2015

Formula

a(n) = A006530(A000217(n)).

Extensions

Edited by Peter Munn, Sep 14 2023