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%I #22 May 13 2020 08:52:25
%S 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,
%T 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,
%U 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
%N 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.
%C Indices n such that a(n) is not equal to 1 are listed in A121594.
%C 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.
%C A compressed version of this sequence (all 1 entries are excluded) is A121595.
%H Alexander Adamchuk, <a href="/A119788/b119788.txt">Table of n, a(n) for n = 1..400</a>
%F a(n) = numerator(n*Sum_{i=1..n} (-1)^(i+1)*1/i) / numerator(Sum_{i=1..n}(-1)^(i+1)*1/i).
%F a(n) = A119787(n) / A058313(n).
%t 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}]]
%Y Cf. A058313, A092579, A119787, A121594, A121595.
%K frac,nonn
%O 1,15
%A _Alexander Adamchuk_, Jun 26 2006, Sep 21 2006
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