A057643 Least common multiple of all (k+1)'s, where the k's are the positive divisors of n.

2, 6, 4, 30, 6, 84, 8, 90, 20, 66, 12, 5460, 14, 120, 48, 1530, 18, 7980, 20, 2310, 88, 276, 24, 81900, 78, 378, 140, 3480, 30, 114576, 32, 16830, 204, 630, 72, 3838380, 38, 780, 280, 284130, 42, 397320, 44, 4140, 5520, 1128, 48, 9746100, 200, 14586, 468

Offset: 1

Author

Leroy Quet, Oct 11 2000

Keywords

• nonn

Comments

a(n) is a divisor of A020696(n). - Ivan Neretin, May 27 2015

Examples

			Since the positive divisors of 6 are 1, 2, 3 and 6, a(6) = LCM(1+1,2+1,3+1,6+1) = LCM(2,3,4,7) = 84.
		

Links

• Carl R. White, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A119250.

Cf. A020696 (product instead of LCM).

Programs

Maple

f:= n -> ilcm(op(map(`+`,numtheory:-divisors(n),1)));
seq(f(n),n=1..100); # Robert Israel, Jul 24 2014

Mathematica

a057643[n_Integer] := Apply[LCM, Map[# + 1 &, Divisors[n]]]; Table[a057643[n], {n, 10000}] (* Michael De Vlieger, Jul 19 2014 *)

PARI

a(n)=lcm(apply(d->d+1,divisors(n))) \\ Charles R Greathouse IV, Feb 14 2013

Python

from math import lcm
from sympy import divisors
def A057643(n): return lcm(*(d+1 for d in divisors(n,generator=True))) # Chai Wah Wu, Jun 30 2022