A348497 a(n) = gcd(A003415(n), A347130(n)), where A003415 is the arithmetic derivative and A347130 is its Dirichlet convolution with the identity function.

0, 1, 1, 2, 1, 5, 1, 12, 3, 7, 1, 16, 1, 9, 8, 16, 1, 21, 1, 24, 10, 13, 1, 44, 5, 15, 27, 32, 1, 31, 1, 80, 14, 19, 12, 30, 1, 21, 16, 68, 1, 41, 1, 48, 39, 25, 1, 112, 7, 45, 20, 56, 1, 81, 16, 92, 22, 31, 1, 92, 1, 33, 51, 96, 18, 61, 1, 72, 26, 59, 1, 156, 1, 39, 55, 80, 18, 71, 1, 176, 54, 43, 1, 124, 22, 45

Offset: 1

Author

Antti Karttunen, Oct 23 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A003557, A347130, A348498.

Cf. also A348492, A348495.

Programs

Mathematica

f[n_] := If[n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[n]]]; Table[GCD[f[n], DivisorSum[n, # f[n/#] &]], {n, 86}] (* Michael De Vlieger, Oct 25 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A347130(n) = sumdiv(n,d,d*A003415(n/d));
A348497(n) = gcd(A003415(n), A347130(n));

Formula

a(n) = gcd(A003415(n), A347130(n)).

a(n) = A003557(n) * A348498(n).