A348492 Greatest common divisor of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).

1, 1, 1, 4, 1, 5, 1, 4, 3, 1, 1, 8, 1, 3, 1, 16, 1, 21, 1, 24, 5, 1, 1, 4, 5, 15, 27, 8, 1, 1, 1, 16, 7, 1, 3, 12, 1, 3, 1, 4, 1, 1, 1, 24, 3, 5, 1, 16, 7, 15, 5, 8, 1, 81, 1, 4, 1, 1, 1, 4, 1, 3, 3, 64, 9, 1, 1, 24, 1, 1, 1, 12, 1, 3, 5, 8, 3, 1, 1, 16, 27, 1, 1, 4, 11, 15, 1, 140, 1, 3, 5, 24, 1, 1, 3, 16, 1, 7

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, A003557, A018804, A348493, A348494.

Cf. also A342413, A342458, A348495.

Programs

Mathematica

Array[GCD[Total@ GCD[#, Range[#]], # Total[#2/#1 & @@@ FactorInteger[#]]] &, 98] (* 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
A348492(n) = gcd(A003415(n), A018804(n));

Formula

a(n) = gcd(A003415(n), A018804(n)).

For n > 1, a(n) = A003415(n) / A348493(n).

a(n) = A003557(n) * A348494(n).