A119788 -id:A119788 - cp's OEIS frontend

A121595 Compressed version of A119788 (all entries equal to 1 are excluded).

5, 7, 5, 11, 13, 17, 7, 29, 7, 37, 19, 47, 119, 41, 23, 5, 29, 31, 11, 37, 37, 41, 43, 71, 13, 7, 13, 13, 47, 13, 49, 7, 7, 7, 53, 5, 79, 59, 97, 61, 71, 103, 67, 17, 71, 61, 73, 139, 17, 17, 79, 19, 19, 19, 83, 19, 151, 89, 29, 29, 263, 97

Offset: 1

Alexander Adamchuk, Aug 09 2006

nonn

Also the ratio of the numerators of n*H'(n) = A119787(n) and H'(n) = A058313(n) when they are different. (H'(n) is the alternating harmonic number H'(n) = Sum_{k=1..n} (-1)^(k+1)*1/k.)
The ratio of numerators A119787(n)/A058313(n) for n = 1..400 is given in A119788(n).
It appears that most a(n) are prime divisors of the corresponding indices A121594(n).
The first and only composite a(n) up to A119788(6000) is a(31) = 49 corresponding to A119788(1470).
It appears that all a(n) belong to A092579(n), which is a sieve using the Fibonacci sequence over the integers >= 2.  [Edited by Petros Hadjicostas, May 11 2020]

Cf. A058313, A092579, A119787, A119788, A121594.

Do[H=Sum[(-1)^(i+1)*1/i, {i, 1, n}]; a=Numerator[n*H]; b=Numerator[H]; If[ !Equal[a,b],Print[{n,a/b}]], {n,1,6000}]

a(n) = A119788(A121594(n)), while the corresponding indices are given in A121594(n).

A121594 Numbers k such that k does not divide the denominator of the k-th alternating Harmonic number.

Original entry on oeis.org

15, 28, 75, 77, 104, 187, 196, 203, 210, 222, 228, 235, 238, 328, 345, 375, 551, 620, 847, 888, 1036, 1107, 1204, 1349, 1352, 1372, 1391, 1430, 1457, 1469, 1470, 1498, 1666, 1687, 1855, 1875, 2133, 2301, 2425, 2440, 2556, 2678, 2948, 3179, 3337, 3477

Offset: 1

Alexander Adamchuk, Aug 09 2006

nonn

Indices k such that A119788(k) is not equal to 1.

Also indices k such that numerators of k*H'(k) = A119787(k) and H'(k) = A058313(k) are different (H'(k) is the alternating harmonic number H'(k) = Sum_{j=1..k} (-1)^(j+1)*1/j). The ratio of numerators A119787(k)/A058313(k) for k = 1..400 is given in A119788(k). A121595(k) = A119788(a(k)) is the compressed version of A119788(k) (all 1 entries are excluded).

Giovanni Resta, Table of n, a(n) for n = 1..900

Cf. A119788, A119787, A058313, A121595.

Cf. A058312 = Denominator of the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k. A074791 = numbers k such that k does not divide the denominator of the k-th Harmonic number.

Do[H=Sum[(-1)^(i+1)*1/i, {i, 1, n}]; a=Numerator[n*H]; b=Numerator[H]; If[ !Equal[a,b],Print[{n,a/b}]],{n,1,6000}]
f=0;Do[f=f+(-1)^(n+1)/n;If[ !IntegerQ[Denominator[f]/n],Print[n]],{n,1,100}] (* Alexander Adamchuk, Jan 02 2007 *)

A119787 Numerator of the product of n and the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.

Original entry on oeis.org

1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 261395, 95549, 1768477, 1632341, 33464927, 155685007, 166770367, 156188887, 3825136961, 3602044091, 19081066231, 18051406831, 57128792093, 54260455193

Offset: 1

Alexander Adamchuk, Jun 26 2006

a(n) almost always equals A058313(n), which is the numerator of the n-th alternating harmonic number, Sum ((-1)^(k+1)/k, k=1..n), except for n = 15, 28, 75, 77, 104, ... The ratio a(n)/A058313(n) for n = 1..400 is given in A119788.

			The first few fractions are 1, 1, 5/2, 7/3, 47/12, 37/10, 319/60, 533/105, 1879/280, ... = A119787/A334721. - _Petros Hadjicostas_, May 08 2020

Cf. A058313, A119788, A334721 (denominators).

Numerator[Table[Sum[(-1)^(i+1)*n/i, {i, 1, n}],{n,1,50}]]

a(n) = numerator(n*sum(k=1, n, (-1)^(k+1)/k)); \\ Michel Marcus, May 09 2020

a(n) = numerator(Sum_{k=1..n} (-1)^(k+1)*n/k).

cp's OEIS Frontend

A121595 Compressed version of A119788 (all entries equal to 1 are excluded).

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A121594 Numbers k such that k does not divide the denominator of the k-th alternating Harmonic number.

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A119787 Numerator of the product of n and the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.

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