A342919 a(n) = A003415(n) / gcd(A001615(n), A003415(n)), where A001615 is Dedekind psi, and A003415 is the arithmetic derivative of n.

0, 1, 1, 2, 1, 5, 1, 1, 1, 7, 1, 2, 1, 3, 1, 4, 1, 7, 1, 2, 5, 13, 1, 11, 1, 5, 3, 2, 1, 31, 1, 5, 7, 19, 1, 5, 1, 7, 2, 17, 1, 41, 1, 2, 13, 25, 1, 7, 1, 1, 5, 2, 1, 3, 2, 23, 11, 31, 1, 23, 1, 11, 17, 2, 3, 61, 1, 2, 13, 59, 1, 13, 1, 13, 11, 2, 3, 71, 1, 11, 1, 43, 1, 31, 11, 15, 4, 35, 1, 41, 5, 2, 17, 49, 1, 17, 1, 11, 25

Offset: 1

Author

Antti Karttunen, Mar 29 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A001615, A003415, A342001, A342458, A342459.

Cf. also A342414.

Programs

PARI

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342919(n) = { my(u=A003415(n)); (u/gcd(u, A001615(n))); };

Formula

a(n) = A003415(n) / A342458(n) = A003415(n) / gcd(A001615(n), A003415(n)).

a(n) = A342001(n) / A342459(n).