A343556 - OEIS

%I #18 May 01 2021 01:30:16

%S 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,

%T 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,

%U 31,7,3,65,33,2,17,69,35,2,3,2,37,15,19,77,13

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

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

%e max(-1/2) = -1/2 therefore a(2) = 2,

%e max(1/2, -2/3) = 1/2 therefore a(3) = 2,

%e max(-1/2, 1/3, -1/4) = 1/3 therefore a(4) = 3,

%e max(1/2, 1/3, 1/4, -4/5) = 1/2 therefore a(5) = 2

%e max(-1/2, -2/3, -1/4, 1/5, 1/3) = 1/3 therefore a(6) = 3,

%e max(1/2, 1/3, 1/4, 1/5, 1/6, -6/7) = 1/2 therefore a(7) = 2,

%e max(-1/2, 1/3, -1/4, 1/5, -1/6, 1/7, -1/8) = 1/3 therefore a(8) = 3,

%e max(1/2, -2/3, 1/4, 1/5, -1/3, 1/7, 1/8, -2/9) = 1/2 therefore a(9) = 2,

%e 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.

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

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

%K nonn,frac

%O 2,1

%A _Mats Granvik_, Apr 19 2021