A121595 -id:A121595 - cp's OEIS frontend

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

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 *)

A119788 Ratio of the numerator of the product of n and the n-th alternating harmonic number nH'(n) to the numerator of the n-th alternating harmonic number H'(n) = Sum_{k=1..n} (-1)^(k+1)1/k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13

Offset: 1

Alexander Adamchuk, Jun 26 2006, Sep 21 2006

Indices n such that a(n) is not equal to 1 are listed in A121594.
It appears that most a(n) > 1 are a prime divisor of their corresponding indices A121594(n). The first and only composite term up to a(6000) is a(1470) = 49 that also divides its index.
A compressed version of this sequence (all 1 entries are excluded) is A121595.

Alexander Adamchuk, Table of n, a(n) for n = 1..400

Cf. A058313, A092579, A119787, A121594, A121595.

Numerator[Table[n*Sum[(-1)^(i+1)*1/i, {i, 1, n}],{n,1,600}]]/Numerator[Table[Sum[(-1)^(i+1)*1/i, {i, 1, n}], {n,1,600}]]

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

a(n) = A119787(n) / A058313(n).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A119788 Ratio of the numerator of the product of n and the n-th alternating harmonic number nH'(n) to the numerator of the n-th alternating harmonic number H'(n) = Sum_{k=1..n} (-1)^(k+1)1/k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A119788 Ratio of the numerator of the product of n and the n-th alternating harmonic number n*H'(n) to the numerator of the n-th alternating harmonic number H'(n) = Sum_{k=1..n} (-1)^(k+1)*1/k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A119788 Ratio of the numerator of the product of n and the n-th alternating harmonic number nH'(n) to the numerator of the n-th alternating harmonic number H'(n) = Sum_{k=1..n} (-1)^(k+1)1/k.