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

%I A343556 #22 Jan 28 2025 15:30:23
%S A343556 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 A343556 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 A343556 31,7,3,65,33,2,17,69,35,2,3,2,37,15,19,77,13
%N A343556 a(n) = denominator(max_{k=2..n}(A191898(n, k)/k)), n>=2.
%H A343556 Antti Karttunen, <a href="/A343556/b343556.txt">Table of n, a(n) for n = 2..20000</a>
%F A343556 n>=2: a(n) = denominator(max_{k=2..n}(A191898(n, k)/k)).
%e A343556 max(-1/2) = -1/2 therefore a(2) = 2,
%e A343556 max(1/2, -2/3) = 1/2 therefore a(3) = 2,
%e A343556 max(-1/2, 1/3, -1/4) = 1/3 therefore a(4) = 3,
%e A343556 max(1/2, 1/3, 1/4, -4/5) = 1/2 therefore a(5) = 2
%e A343556 max(-1/2, -2/3, -1/4, 1/5, 1/3) = 1/3 therefore a(6) = 3,
%e A343556 max(1/2, 1/3, 1/4, 1/5, 1/6, -6/7) = 1/2 therefore a(7) = 2,
%e A343556 max(-1/2, 1/3, -1/4, 1/5, -1/6, 1/7, -1/8) = 1/3 therefore a(8) = 3,
%e A343556 max(1/2, -2/3, 1/4, 1/5, -1/3, 1/7, 1/8, -2/9) = 1/2 therefore a(9) = 2,
%e A343556 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 A343556 a[n_] := DivisorSum[n, MoebiusMu[#] # &]; nn = 78; Denominator[Table[Max[Table[a[GCD[n, k]]/k, {k, 2, n}]], {n, 2, nn}]]
%o A343556 (PARI)
%o A343556 memoA191898 = Map();
%o A343556 A191898sq(n, k) = if(n<1 || k<1, 0, n==1 || k==1, 1, k>n, A191898sq(k, n), k<n, A191898sq(k, (n-1)%k+1), my(v); if(mapisdefined(memoA191898,[n,k],&v), v, v = -sum( i=1, n-1, A191898sq(n, i)); mapput(memoA191898,[n,k],v); (v))); \\ After _Michael Somos_' code in A191898
%o A343556 A343556(n) = { my(m=0,r); for(k=2, n, r = A191898sq(n, k)/k; if(!m || (r > m), m = r)); denominator(m); }; \\ _Antti Karttunen_, Jan 28 2025
%Y A343556 Cf. A343555 (numerators). Cf. A171462, A191898.
%K A343556 nonn,frac
%O A343556 2,1
%A A343556 _Mats Granvik_, Apr 19 2021