A322318 a(n) = gcd(A003557(n), A048250(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 3, 2, 1, 1, 1, 2, 1

Offset: 1

Author

Antti Karttunen, Dec 05 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001615, A003557, A048250, A322319.

Cf. also A066086, A322320.

Programs

Mathematica

a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, GCD[ 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]));
A322318(n) = gcd(A048250(n), A003557(n));

Formula

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

a(n) = A001615(n) / A322319(n).