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A300721
Möbius transform of A060681, the largest difference between consecutive divisors of n (ordered by size).
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 11 2018
STATUS
approved