A343556 a(n) = denominator(max_{k=2..n}(A191898(n, k)/k)), n>=2.

2, 2, 3, 2, 3, 2, 3, 2, 5, 2, 3, 2, 7, 15, 3, 2, 3, 2, 5, 7, 11, 2, 3, 2, 13, 2, 7, 2, 15, 2, 3, 33, 17, 35, 3, 2, 19, 13, 5, 2, 7, 2, 11, 15, 23, 2, 3, 2, 5, 51, 13, 2, 3, 11, 7, 19, 29, 2, 15, 2, 31, 7, 3, 65, 33, 2, 17, 69, 35, 2, 3, 2, 37, 15, 19, 77, 13

Offset

2,1

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A343555 (numerators). Cf. A171462, A191898.

Sequence in context: A029374 A255933 A340805 * A319396 A049237 A162361

Adjacent sequences: A343553 A343554 A343555 * A343557 A343558 A343559

Keyword

nonn,frac

Author

Mats Granvik, Apr 19 2021

Status

approved