A277440 Denominators of a sequence defined by a modified recurrence for the exponential of the von Mangoldt function.

1, 1, 2, 1, 6, 1, 24, 3, 40, 3, 120, 1, 42, 5, 224, 5, 2592, 1, 540, 7, 220, 7, 4224, 5, 19968, 27, 728, 81, 1575, 1, 230400, 11, 8704, 77, 1377, 35, 18468, 13, 3891200, 13, 18063360, 1, 698544, 3645, 253, 3645, 5087232, 7, 307200

Offset

1,3

Comments

See A277439 for the conjecture about the average of twin primes A014574 and the ratio A277439(n)/A277440(n).

Links

Table of n, a(n) for n=1..49.

Formula

Denominators of a ratio that is the first column of the array (T(n,k): n,k >= 1), which is defined by the following recurrence:

T(1,1) = 1.

T(n,k) = if k = 1 then n/(Product_{i=1..n-1}(T(n + 1, k + i)))/(Product_{i=1..n-1}(T(n - 1, k + i))) else if(mod(n, k) = 0 then T(n/k, 1) else 1) else 1).

Mathematica

Clear[t]; nn = 49; t[1, 1] = 1; t[n_, k_] := t[n, k] = If[k == 1, n/Product[t[n + 1, k + i], {i, 1, n - 1}]/Product[t[n - 1, 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. A014574, A277439 (numerators).

Sequence in context: A186283 A307374 A173279 * A321597 A083720 A369925

Adjacent sequences: A277437 A277438 A277439 * A277441 A277442 A277443

Keyword

nonn,frac

Author

Mats Granvik, Oct 15 2016

Status

approved