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

1,4

Links

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

Formula

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

a(n) = -Sum_{d|n, d<n} A008683(n/d) * A344695(d).

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
A344695(n) = gcd(sigma(n), A001615(n));
A347231(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A344695(d));

Crossrefs

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

Cf. also A347229.

Sequence in context: A317855 A301331 A301333 * A213670 A116609 A124846

Adjacent sequences: A347228 A347229 A347230 * A347232 A347233 A347234

Keyword

sign

Author

Antti Karttunen, Aug 25 2021

Status

approved