A322351 a(n) = min(A003557(n), A173557(n)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 2, 6, 4, 1, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 6, 3, 4, 1, 1, 1, 4, 1

Offset: 1

Author

Antti Karttunen, Dec 05 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000010, A003557, A173557, A322320, A322321, A322352, A322355.

Programs

Mathematica

a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, Min[ 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
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A322351(n) = min(A003557(n), A173557(n));

Formula

a(n) = min(A003557(n), A173557(n)).

a(n) = A000010(n) / A322352(n).