A238162 Least common multiple of the prime factors of n, each increased by 1.

3, 4, 3, 6, 12, 8, 3, 4, 6, 12, 12, 14, 24, 12, 3, 18, 12, 20, 6, 8, 12, 24, 12, 6, 42, 4, 24, 30, 12, 32, 3, 12, 18, 24, 12, 38, 60, 28, 6, 42, 24, 44, 12, 12, 24, 48, 12, 8, 6, 36, 42, 54, 12, 12, 24, 20, 30, 60, 12, 62, 96, 8, 3, 42, 12, 68, 18, 24, 24, 72, 12, 74, 114, 12, 60, 24, 84, 80, 6, 4, 42, 84, 24, 18, 132, 60, 12, 90, 12, 56, 24, 32, 48, 60, 12, 98, 24, 12, 6

Offset: 2

Author

Joseph L. Pe, Feb 18 2014

Keywords

• nonn

Comments

If n is prime, then a(n) = n + 1. - Wesley Ivan Hurt, Apr 05 2014

If n is a composite squarefree number and a(n) divides n+1, then n is a Lucas-Carmichael number (A006972). - Daniel Suteu, Oct 02 2022

Examples

			The prime factors of 6 are 2 and 3, which become 3 and 4 when respectively increased by 1, and lcm(3, 4) = 12. Therefore, a(6) = 12.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A006972.

Programs

PARI

a(n) = my(f=factor(n)); lcm(vector(#f~, k, f[k, 1]+1)); \\ Daniel Suteu, Oct 02 2022