A300721 Möbius transform of A060681, the largest difference between consecutive divisors of n (ordered by size).

0, 1, 2, 1, 4, 0, 6, 2, 4, 0, 10, 2, 12, 0, 4, 4, 16, 2, 18, 4, 6, 0, 22, 4, 16, 0, 12, 6, 28, 4, 30, 8, 10, 0, 18, 6, 36, 0, 12, 8, 40, 6, 42, 10, 16, 0, 46, 8, 36, 4, 16, 12, 52, 6, 30, 12, 18, 0, 58, 8, 60, 0, 24, 16, 36, 10, 66, 16, 22, 6, 70, 12, 72, 0, 24, 18, 50, 12, 78, 16, 36, 0, 82, 12, 48, 0, 28, 20, 88, 8, 60, 22, 30, 0, 54, 16

Offset: 1

Author

Antti Karttunen, Mar 11 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A008683, A060681, A300236, A300722, A322873 (ordinal transform).

Programs

Mathematica

A060681[n_] := n - n/FactorInteger[n][[1, 1]];
a[n_] := Sum[MoebiusMu[n/d]*A060681[d], {d, Divisors[n]}];
Array[a, 100] (* Jean-François Alcover, Jan 07 2022 *)

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A060681(n) = (n-A032742(n));
A300721(n) = sumdiv(n,d,moebius(n/d)*A060681(d));

Formula

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

a(n) = A060681(n) - A300722(n).

a(n) = A000010(n) - A300236(n).