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

1,2

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.

Formula

From Amiram Eldar, May 16 2025: (Start)

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A014493, A020639, A042963, A069901.

Sequence in context: A339971 A156724 A196186 * A006166 A339718 A349926

Adjacent sequences: A075750 A075751 A075752 * A075754 A075755 A075756

Keyword

nonn,easy

Author

Reinhard Zumkeller, Mar 11 2003

Extensions

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

Status

approved