A300722 Difference between A060681 (largest difference between consecutive divisors of n as ordered by size) and its Möbius transform.

0, 0, 0, 1, 0, 3, 0, 2, 2, 5, 0, 4, 0, 7, 6, 4, 0, 7, 0, 6, 8, 11, 0, 8, 4, 13, 6, 8, 0, 11, 0, 8, 12, 17, 10, 12, 0, 19, 14, 12, 0, 15, 0, 12, 14, 23, 0, 16, 6, 21, 18, 14, 0, 21, 14, 16, 20, 29, 0, 22, 0, 31, 18, 16, 16, 23, 0, 18, 24, 29, 0, 24, 0, 37, 26, 20, 16, 27, 0, 24, 18, 41, 0, 30, 20, 43, 30, 24, 0, 37, 18, 24, 32, 47, 22, 32

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A060681(d).

a(n) = A060681(n) - A300721(n).

Prog

(PARI)
A032742(n) = if(1==n, n, n/vecmin(factor(n)[, 1]));
A060681(n) = (n-A032742(n));
A300722(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A060681(d));

Crossrefs

Sequence in context: A290566 A285006 A369747 * A087625 A300720 A280238

Adjacent sequences: A300719 A300720 A300721 * A300723 A300724 A300725

Keyword

nonn

Author

Antti Karttunen, Mar 11 2018

Status

approved