A238162 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

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

LINKS

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

EXAMPLE

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.

PROG

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