A322319 a(n) = lcm(A003557(n), A048250(n)).

1, 3, 4, 6, 6, 12, 8, 12, 12, 18, 12, 12, 14, 24, 24, 24, 18, 12, 20, 18, 32, 36, 24, 12, 30, 42, 36, 24, 30, 72, 32, 48, 48, 54, 48, 12, 38, 60, 56, 36, 42, 96, 44, 36, 24, 72, 48, 24, 56, 90, 72, 42, 54, 36, 72, 24, 80, 90, 60, 72, 62, 96, 96, 96, 84, 144, 68, 54, 96, 144, 72, 12, 74, 114, 120, 60, 96, 168, 80, 72

Offset: 1

Author

Antti Karttunen, Dec 05 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to lcm's

Crossrefs

Cf. A001615, A003557, A048250, A322318.

Cf. also A322321, A322359.

Programs

Mathematica

a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, LCM[ Times@@ (First[#] ^(Last[#]-1)& /@  f), Times@@((#+1)& @@@ f)]]]; Array[a, 120] (* Amiram Eldar, Dec 05 2018 *)

PARI

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A322319(n) = lcm(A048250(n), A003557(n));

Formula

a(n) = lcm(A003557(n), A048250(n)).

a(n) = A001615(n) / A322318(n).