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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A119250.

Cf. A020696 (product instead of LCM).

Sequence in context: A006233 A164020 A326579 * A073039 A322792 A253588

Adjacent sequences: A057640 A057641 A057642 * A057644 A057645 A057646

Keyword

nonn

Author

Leroy Quet, Oct 11 2000

Status

approved