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Least common multiple of product (p-1) and product (p+1), where p ranges over distinct prime divisors of n.
5

%I #12 Dec 05 2018 08:00:55

%S 1,3,4,3,12,12,24,3,4,36,60,12,84,24,24,3,144,12,180,36,96,180,264,12,

%T 12,84,4,24,420,72,480,3,240,432,48,12,684,180,168,36,840,96,924,180,

%U 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

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

%H Antti Karttunen, <a href="/A322359/b322359.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

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

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

%t 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 *)

%o (PARI)

%o A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));

%o A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));

%o A322359(n) = lcm(A048250(n), A173557(n));

%Y Cf. A048250, A066086, A173557, A322360.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 04 2018