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A277440 Denominators of a sequence defined by a modified recurrence for the exponential of the von Mangoldt function. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A055878

Adjacent sequences:  A277437 A277438 A277439 * A277441 A277442 A277443

KEYWORD

nonn,frac

AUTHOR

Mats Granvik, Oct 15 2016

STATUS

approved

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)