A347235 Dirichlet convolution of Euler phi with A342001, where A342001(n) = A003415(n) / A003557(n).

0, 1, 1, 3, 1, 8, 1, 7, 4, 12, 1, 21, 1, 16, 14, 15, 1, 27, 1, 33, 18, 24, 1, 47, 6, 28, 13, 45, 1, 87, 1, 31, 26, 36, 22, 69, 1, 40, 30, 75, 1, 119, 1, 69, 51, 48, 1, 99, 8, 63, 38, 81, 1, 84, 30, 103, 42, 60, 1, 219, 1, 64, 67, 63, 34, 183, 1, 105, 50, 183, 1, 153, 1, 76, 75, 117, 34, 215, 1, 159, 40, 84, 1, 303, 42

Offset: 1

Author

Antti Karttunen, Aug 26 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000010, A003415, A003557, A342001.

Cf. also A346485, A347131, A347233, A347234, A347395.

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]));
A342001(n) = (A003415(n) / A003557(n));
A347235(n) = sumdiv(n,d,eulerphi(d)*A342001(n/d));

PARI

A347235(n) = sum(k=1,n,A342001(gcd(n,k))); \\ (Slow) - Antti Karttunen, Sep 02 2021

Formula

a(n) = Sum_{d|n} A000010(n/d) * A342001(d).

a(n) = Sum_{k=1..n} A342001(gcd(n,k)). - Antti Karttunen, Sep 02 2021