A075753 Smallest prime factor of n-th odd triangular number; a(1) = 1.

1, 3, 3, 3, 3, 5, 7, 3, 3, 3, 3, 11, 5, 3, 3, 3, 3, 5, 19, 3, 3, 3, 3, 23, 5, 3, 3, 3, 3, 29, 31, 3, 3, 3, 3, 5, 37, 3, 3, 3, 3, 41, 5, 3, 3, 3, 3, 5, 7, 3, 3, 3, 3, 53, 5, 3, 3, 3, 3, 7, 11, 3, 3, 3, 3, 5, 7, 3, 3, 3, 3, 11, 5, 3, 3, 3, 3, 5, 79, 3, 3, 3, 3, 83, 5, 3, 3, 3, 3, 89, 7, 3, 3, 3, 3, 5, 97, 3, 3, 3

Offset: 1

Author

Reinhard Zumkeller, Mar 11 2003

Keywords

• nonn
• easy

Comments

As A014493(n) = binomial(A042963(n),2) and a(n) = A020639(A014493(n)) > 2 for n > 1, A014493(n) is a good binomial coefficient.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Good Binomial Coefficient.
• Eric Weisstein's World of Mathematics, Least Prime Factor.
• Eric Weisstein's World of Mathematics, Triangular Number.

Crossrefs

Cf. A014493, A020639, A042963, A069901.

Programs

Mathematica

FactorInteger[#][[1, 1]]&/@Select[Accumulate[Range[200]], OddQ] (* Harvey P. Dale, Jul 30 2016 *)

PARI

a(n) = if(n == 1, 1, factor((2*n-1)*(2*n-1-(-1)^n)/2)[1,1]); \\ Amiram Eldar, May 16 2025

Formula

From Amiram Eldar, May 16 2025: (Start)

a(n) = A020639(A014493(n)).

a(n) = A069901(A042963(n)). (End)

Extensions

a(1) inserted by Amiram Eldar, May 16 2025