A340191 Difference between A063994 and its Möbius transform.

0, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 6, 5, 1, 1, 1, 1, 1, 7, 10, 1, 1, 4, 12, 2, 1, 1, 0, 1, 1, 11, 16, 9, 1, 1, 18, 13, 1, 1, -2, 1, 1, 4, 22, 1, 1, 6, 1, 17, 1, 1, 1, 13, 3, 19, 28, 1, 1, 1, 30, 4, 1, 15, -6, 1, 1, 23, -4, 1, 1, 1, 36, 4, 1, 15, -8, 1, 1, 2, 40, 1, 3, 19, 42, 29, 1, 1, 5, 17, 1, 31, 46, 21

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

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

Formula

a(n) = A063994(n) - A340190(n).

a(n) = -Sum_{d|n, d<n} A008683(n/d) * A063994(d).

Prog

(PARI)
A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
A340191(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A063994(d));

Crossrefs

Cf. A008683, A063994, A340190.

Sequence in context: A318622 A353785 A245195 * A182105 A023506 A232089

Adjacent sequences: A340188 A340189 A340190 * A340192 A340193 A340194

Keyword

sign

Author

Antti Karttunen, Dec 31 2020

Status

approved