A343555 a(n) = numerator(max_{k=2..n}(A191898(n, k)/k)), n>=2.

-1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 8, 1, 1, 1, 1, 2, 4, 5, 1, 1, 1, 6, 1, 3, 1, 8, 1, 1, 20, 8, 24, 1, 1, 9, 8, 2, 1, 4, 1, 5, 8, 11, 1, 1, 1, 2, 32, 6, 1, 1, 8, 3, 12, 14, 1, 8, 1, 15, 4, 1, 48, 20, 1, 8, 44, 24, 1, 1, 1, 18, 8, 9, 60, 8

Offset

2,9

Links

Table of n, a(n) for n=2..78.

Formula

n>=2: a(n) = numerator(max_{k=2..n}(A191898(n, k)/k)).

Example

max(-1/2) = -1/2 therefore a(2) = -1,
max(1/2, -2/3) = 1/2 therefore a(3) = 1,
max(-1/2, 1/3, -1/4) = 1/3 therefore a(4) = 1,
max(1/2, 1/3, 1/4, -4/5) = 1/2 therefore a(5) = 1
max(-1/2, -2/3, -1/4, 1/5, 1/3) = 1/3 therefore a(6) = 1,
max(1/2, 1/3, 1/4, 1/5, 1/6, -6/7) = 1/2 therefore a(7) = 1,
max(-1/2, 1/3, -1/4, 1/5, -1/6, 1/7, -1/8) = 1/3 therefore a(8) = 1,
max(1/2, -2/3, 1/4, 1/5, -1/3, 1/7, 1/8, -2/9) = 1/2 therefore a(9) = 1,
max(-1/2, 1/3, -1/4, -4/5, -1/6, 1/7, -1/8, 1/9, 2/5) = 2/5 therefore a(10) = 2.

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] # &]; nn = 78; Numerator[
Table[Max[Table[a[GCD[n, k]]/k, {k, 2, n}]], {n, 2, nn}]]

Crossrefs

Cf. A343556 (denominator). Cf. A171462, A191898.

Sequence in context: A259844 A112707 A196017 * A251660 A279453 A054252

Adjacent sequences: A343552 A343553 A343554 * A343556 A343557 A343558

Keyword

frac,sign

Author

Mats Granvik, Apr 19 2021

Status

approved