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

1,6

Comments

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

Links

Table of n, a(n) for n=1..60.

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)).

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]

Crossrefs

Cf. A276835, A006512, A014963.

Sequence in context: A291326 A291325 A116512 * A291324 A075388 A036445

Adjacent sequences: A276833 A276834 A276835 * A276837 A276838 A276839

Keyword

nonn,frac,more

Author

Mats Granvik, Sep 20 2016

Status

approved