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

1,2

Comments

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

Links

Table of n, a(n) for n=1..66.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Cf. A000217, A006530, A074399.

Sequence in context: A172170 A233808 A141424 * A335568 A085779 A078936

Adjacent sequences: A069899 A069900 A069901 * A069903 A069904 A069905

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 10 2002

Extensions

Edited by Peter Munn, Sep 14 2023

Status

approved