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A330680 Numbers that begin a run of consecutive integers k such that the denominator of the k-th harmonic number is lcm(1..k). 1

%I

%S 1,9,27,49,88,125,243,289,361,484,841,968,1164,1331,1369,2401,3125,

%T 3488,3721,6889,7085,7761,7921,8342,8502,9156,10648,19683,22208,22801,

%U 25886,28561,29929,30877,32041,32761,33178,36481,59049,83521,87079,88307,92199

%N Numbers that begin a run of consecutive integers k such that the denominator of the k-th harmonic number is lcm(1..k).

%C A098464 lists the numbers k such that lcm(1,2,3,...,k) equals the denominator of the k-th harmonic number H(k) = 1/1 + 1/2 + 1/3 + ... + 1/k.

%H Chai Wah Wu, <a href="/A330680/b330680.txt">Table of n, a(n) for n = 1..308</a>

%e The numbers k such that the denominator of the k-th harmonic number equals lcm(1..k) begin with the following runs of consecutive integers:

%e 1, 2, 3, 4, 5;

%e 9, 10, 11, 12, 13, 14, 15, 16, 17;

%e 27, 28, 29, 30, 31, 32;

%e 49, 50, 51, 52, 53;

%e 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99;

%e 125, 126, 127, ...

%e so this sequence begins 1, 9, 27, 49, 88, 125, ...

%Y Cf. A002805 (denominator of H(n)), A003418 (lcm(1..n)), A098464 (numbers k such that A002805(k)=A003418(k)).

%K nonn

%O 1,2

%A _Jon E. Schoenfield_, Dec 24 2019

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Last modified May 11 06:28 EDT 2021. Contains 343784 sequences. (Running on oeis4.)