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

1,4

Links

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

Formula

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

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

Prog

(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))); };

Crossrefs

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

Cf. also A342414.

Sequence in context: A175178 A348494 A256541 * A066421 A369526 A206563

Adjacent sequences: A342916 A342917 A342918 * A342920 A342921 A342922

Keyword

nonn

Author

Antti Karttunen, Mar 29 2021

Status

approved