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Numbers k such that lcm(1..k) equals the denominator of the sum of the first k harmonic numbers.
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%I #10 Mar 15 2018 04:14:49

%S 1,2,4,10,12,16,28,30,52,88,96,126,130,136,138,148,150,250,256,262,

%T 268,270,292,970,976,982,990,996,1008,1012,1018,1020,1030,1032,1038,

%U 1048,1050,1060,1062,1372,1380,1398,1408,1422,1426,1428,1432,1438

%N Numbers k such that lcm(1..k) equals the denominator of the sum of the first k harmonic numbers.

%C k+1 must be a prime, but converse is not true.

%e The sum of the first 4 harmonic numbers is 77/12 and 12 is lcm(1,2,3,4).

%t big=Table[LCM @@Range[n]/Denominator[ -n+(1+n) HarmonicNumber[n]], {n, 2048}]; Position[big, 1]//Flatten

%o (PARI) h(n) = sum(j=1, n, 1/j);

%o isok(n) = lcm(vector(n, k, k)) == denominator(sum(k=1, n, h(k))); \\ _Michel Marcus_, Mar 15 2018

%K nonn

%O 1,2

%A _Wouter Meeussen_, Apr 13 2003

%E More terms from _Wouter Meeussen_, Feb 21 2004