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.

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

Author

Alexander Adamchuk, Jun 26 2006, Sep 21 2006

Keywords

• frac
• nonn

Comments

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.

Links

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

Crossrefs

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

Programs

Mathematica

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}]]

Formula

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).