A347129 a(n) = A347130(n) / A003557(n), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n.

0, 1, 1, 3, 1, 10, 1, 6, 3, 14, 1, 24, 1, 18, 16, 10, 1, 21, 1, 36, 20, 26, 1, 44, 3, 30, 6, 48, 1, 124, 1, 15, 28, 38, 24, 45, 1, 42, 32, 68, 1, 164, 1, 72, 39, 50, 1, 70, 3, 27, 40, 84, 1, 36, 32, 92, 44, 62, 1, 276, 1, 66, 51, 21, 36, 244, 1, 108, 52, 236, 1, 78, 1, 78, 33, 120, 36, 284, 1, 110, 10, 86, 1, 372, 44

Offset: 1

Author

Antti Karttunen, Aug 23 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A003415, A003557, A347126 [= a(A276086(n))], A347130.

Cf. also A342001, A347127, A347128.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A347130(n) = sumdiv(n,d,d*A003415(n/d));
A347129(n) = (A347130(n) / A003557(n));

Formula

a(n) = A347130(n) / A003557(n).