A276836 - OEIS

%I #9 Oct 21 2016 15:16:02

%S 1,1,1,1,1,2,1,3,1,4,3,5,1,6,1,7,15,2,1,9,1,5,21,11,1,2,5,13,9,7,1,15,

%T 1,8,11,17,35,27,1,19,39,5,1,7,1,44,45,69,1,54,7,125,17,39,1,27,55,14,

%U 57,116

%N Denominator of modified von Mangoldt function defined recursively.

%C See A276835 for the conjecture about the ratio A276835(n)/A276836(n).

%F Recurrence for the ratio A276835(n)/A276836(n):

%F t(1, 1) = 1, t(n, k) = if(n/k = 2 then 2 else if(and(k == 1, n >= 3), n/(Product_{i = 1..n-1} t(n, k + i))/(Product_{i = 1..n-1} t(n, k + i)) else if(mod(n, k) = 0 then t(n/k, 1) else 1) else 1)).

%t Clear[t]; nn = 60; t[1, 1] = 1; t[n_, k_] := t[n, k] = If[n/k == 2, 2, If[And[k == 1, n >= 3], n/Product[t[n, k + i], {i, 1, n - 1}]/Product[t[n - 2, k + i], {i, 1, n - 1}],If[Mod[n, k] == 0, t[n/k, 1], 1], 1]]; a = Table[t[n, 1], {n, 1, nn}]; Numerator[a]; Denominator[a]

%Y Cf. A276835, A006512, A014963.

%K nonn,frac,more

%O 1,6

%A _Mats Granvik_, Sep 20 2016