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A119955 Numbers n such that denominator of n-th Harmonic Number equals denominator of n-th Alternative Harmonic Number. 3

%I

%S 1,2,3,4,5,9,10,11,12,13,14,27,49,50,51,52,53,125,126,127,128,129,130,

%T 131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,

%U 148,149,150,151,152,153,154,155,289,290,291,292,293,841,842,843,844

%N Numbers n such that denominator of n-th Harmonic Number equals denominator of n-th Alternative Harmonic Number.

%C Up to n=14 A002805[n] coincides with A058312[n]. a(n) up to a(12)=27 coincides with A096304[n].

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>.

%e Denominators of Harmonic Number (H[n] = Sum[1/i, {i, n}]) are A002805[n] = {1,2,6,12,60,20,140,280,2520,2520,27720,27720,360360,360360,360360,...}.

%e Denominators of Alternative Harmonic Number (H'[n] = Sum[(-1)^(i+1)*1/i, {i, n}]) are A058312[n] = {1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,72072,...}.

%e a(1) = 1 because A002805[1] = A058312[1].

%e 15 is not in a(n) because A002805[15] = 360360 is not equal to A058312[15] = 72072.

%t Do[s1=Denominator[Sum[(-1)^(i+1)*1/i, {i, n}]]; s2=Denominator[Sum[1/i, {i, n}]]; If[Equal[s2, s1], Print[n]], {n, 1, 1500}]

%Y Cf. A002805, A058312, A096304.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, Aug 02 2006

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Last modified September 24 12:17 EDT 2021. Contains 347642 sequences. (Running on oeis4.)