A347231 Difference between A344695 [gcd(psi(n),sigma(n))] and its Möbius transform.

0, 1, 1, 3, 1, 6, 1, 1, 4, 8, 1, 10, 1, 10, 9, 3, 1, 9, 1, 16, 11, 14, 1, 6, 6, 16, 1, 22, 1, 42, 1, 1, 15, 20, 13, -5, 1, 22, 17, 8, 1, 54, 1, 34, 21, 26, 1, 10, 8, 13, 21, 40, 1, 6, 17, 10, 23, 32, 1, 54, 1, 34, 29, 3, 19, 78, 1, 52, 27, 74, 1, 9, 1, 40, 19, 58, 19, 90, 1, 16, 4, 44, 1, 74, 23, 46, 33, 14, 1, 48

Offset: 1

Author

Antti Karttunen, Aug 25 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A000203, A001615, A008683, A344695, A347230.

Cf. also A347229.

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
A344695(n) = gcd(sigma(n), A001615(n));
A347231(n) = -sumdiv(n,d,(dA344695(d));

Formula

a(n) = A344695(n) - A347230(n).

a(n) = -Sum_{d|n, dA008683(n/d) * A344695(d).