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

Author

Antti Karttunen, Mar 11 2018

Keywords

• nonn

Links

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

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A060681(n) = (n-A032742(n));
A300722(n) = -sumdiv(n,d,(dA060681(d));

Formula

a(n) = -Sum_{d|n, dA008683(n/d)*A060681(d).

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