A328823 a(n) is the least prime factor of A000096(n) = n*(n+3)/2.

2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 7, 2, 2, 7, 3, 2, 2, 3, 11, 2, 2, 5, 13, 2, 2, 13, 3, 2, 2, 3, 17, 2, 2, 17, 5, 2, 2, 19, 3, 2, 2, 3, 23, 2, 2, 7, 5, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 29, 31, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 37, 2, 2, 7, 3, 2, 2

Offset: 1

Author

Ali Sada, Oct 28 2019

Keywords

• nonn

Comments

The motivation is that n*(n+3)/2 = n + T(n), where T(n) = n*(n+1)/2 = A000217(n), the triangular numbers.

Examples

			For n = 5, n + T(n) = 5 + 15 = 20. The smallest prime factor of 20 is 2, so a(5) = 2.
		

Crossrefs

Cf. A000096 (n + T(n)), A000217 (triangular numbers), A020639 (smallest prime factor).

Programs

Mathematica

Array[FactorInteger[# (# + 3)/2][[1, 1]] &, 77] (* Amiram Eldar, Nov 02 2019 *)

PARI

A328823(n)=A020639(n*(n+3)/2) \\ M. F. Hasler, Nov 10 2019

Formula

a(n) = A020639(A000096(n)). - Michel Marcus, Oct 28 2019

Extensions

Simpler definition from M. F. Hasler, Nov 10 2019