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

1,3

Links

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

Formula

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

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

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

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 *)

Prog

(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));

Crossrefs

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

Sequence in context: A324546 A033883 A106316 * A126707 A326305 A057458

Adjacent sequences: A300718 A300719 A300720 * A300722 A300723 A300724

Keyword

nonn

Author

Antti Karttunen, Mar 11 2018

Status

approved