A276836 Denominator of modified von Mangoldt function defined recursively.

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, 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, 57, 116

Offset: 1

Author

Mats Granvik, Sep 20 2016

Keywords

• nonn
• frac
• more

Comments

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

Crossrefs

Cf. A276835, A006512, A014963.

Programs

Mathematica

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]

Formula

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

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)).