A121595 - OEIS

%I #9 May 11 2020 19:14:35

%S 5,7,5,11,13,17,7,29,7,37,19,47,119,41,23,5,29,31,11,37,37,41,43,71,

%T 13,7,13,13,47,13,49,7,7,7,53,5,79,59,97,61,71,103,67,17,71,61,73,139,

%U 17,17,79,19,19,19,83,19,151,89,29,29,263,97

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

%C 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.)

%C The ratio of numerators A119787(n)/A058313(n) for n = 1..400 is given in A119788(n).

%C It appears that most a(n) are prime divisors of the corresponding indices A121594(n).

%C The first and only composite a(n) up to A119788(6000) is a(31) = 49 corresponding to A119788(1470).

%C 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]

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

%t 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}]

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

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Aug 09 2006