A322321 a(n) = lcm(A003557(n), A173557(n)).

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 2, 12, 6, 8, 8, 16, 6, 18, 4, 12, 10, 22, 4, 20, 12, 18, 6, 28, 8, 30, 16, 20, 16, 24, 6, 36, 18, 24, 4, 40, 12, 42, 10, 24, 22, 46, 8, 42, 20, 32, 12, 52, 18, 40, 12, 36, 28, 58, 8, 60, 30, 12, 32, 48, 20, 66, 16, 44, 24, 70, 12, 72, 36, 40, 18, 60, 24, 78, 8, 54, 40, 82, 12, 64, 42, 56, 20

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to lcm's

Formula

a(n) = lcm(A003557(n), A173557(n)) = lcm(A322351(n), A322352(n)).

a(n) = A000010(n) / A322320(n).

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 *)

Prog

(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A322321(n) = lcm(A003557(n), A173557(n));

Crossrefs

Cf. A000010, A003557, A173557, A322320, A322351, A322352.

Cf. also A322319, A322359.

Sequence in context: A277030 A011773 A306275 * A080737 A152455 A293484

Adjacent sequences: A322318 A322319 A322320 * A322322 A322323 A322324

Keyword

nonn

Author

Antti Karttunen, Dec 05 2018

Status

approved