A322359 Least common multiple of product (p-1) and product (p+1), where p ranges over distinct prime divisors of n.

1, 3, 4, 3, 12, 12, 24, 3, 4, 36, 60, 12, 84, 24, 24, 3, 144, 12, 180, 36, 96, 180, 264, 12, 12, 84, 4, 24, 420, 72, 480, 3, 240, 432, 48, 12, 684, 180, 168, 36, 840, 96, 924, 180, 24, 792, 1104, 12, 24, 36, 288, 84, 1404, 12, 360, 24, 720, 1260, 1740, 72, 1860, 480, 96, 3, 336, 720, 2244, 432, 1056, 144, 2520, 12

Offset: 1

Author

Antti Karttunen, Dec 04 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to lcm's

Crossrefs

Cf. A048250, A066086, A173557, A322360.

Programs

Mathematica

a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, LCM[Times@@((#-1)& @@@ f), Times@@((#+1)& @@@ f)]]]; Array[a, 100] (* Amiram Eldar, Dec 05 2018 *)

PARI

A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A322359(n) = lcm(A048250(n), A173557(n));

Formula

a(n) = lcm(A048250(n), A173557(n)).

a(n) = A322360(n)/A066086(n).