cp's OEIS Frontend

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

%I A121594 #10 Jun 01 2020 20:47:04
%S A121594 15,28,75,77,104,187,196,203,210,222,228,235,238,328,345,375,551,620,
%T A121594 847,888,1036,1107,1204,1349,1352,1372,1391,1430,1457,1469,1470,1498,
%U A121594 1666,1687,1855,1875,2133,2301,2425,2440,2556,2678,2948,3179,3337,3477
%N A121594 Numbers k such that k does not divide the denominator of the k-th alternating Harmonic number.
%C A121594 Indices k such that A119788(k) is not equal to 1.
%C A121594 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).
%H A121594 Giovanni Resta, <a href="/A121594/b121594.txt">Table of n, a(n) for n = 1..900</a>
%t 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}]
%t A121594 f=0;Do[f=f+(-1)^(n+1)/n;If[ !IntegerQ[Denominator[f]/n],Print[n]],{n,1,100}] (* _Alexander Adamchuk_, Jan 02 2007 *)
%Y A121594 Cf. A119788, A119787, A058313, A121595.
%Y A121594 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.
%K A121594 nonn
%O A121594 1,1
%A A121594 _Alexander Adamchuk_, Aug 09 2006