A348493 a(n) = A003415(n) / gcd(A003415(n), A018804(n)), where A003415 is the arithmetic derivative and A018804 is Pillai's arithmetical function.

0, 1, 1, 1, 1, 1, 1, 3, 2, 7, 1, 2, 1, 3, 8, 2, 1, 1, 1, 1, 2, 13, 1, 11, 2, 1, 1, 4, 1, 31, 1, 5, 2, 19, 4, 5, 1, 7, 16, 17, 1, 41, 1, 2, 13, 5, 1, 7, 2, 3, 4, 7, 1, 1, 16, 23, 22, 31, 1, 23, 1, 11, 17, 3, 2, 61, 1, 3, 26, 59, 1, 13, 1, 13, 11, 10, 6, 71, 1, 11, 4, 43, 1, 31, 2, 3, 32, 1, 1, 41, 4, 4, 34, 49, 8

Offset: 1

Author

Antti Karttunen, Oct 21 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A018804, A348492, A348494.

Programs

Mathematica

Array[#2/GCD[#1, #2] & @@ {Total@ GCD[#, Range[#]], If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]]} &, 95] (* Michael De Vlieger, Oct 21 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A348493(n) = { my(u=A003415(n)); (u/gcd(u,A018804(n))); };

Formula

a(n) = A003415(n) / A348492(n).