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%I #16 Dec 14 2020 05:20:38
%S 3,4,6,7,10,19,20,26,30,31,33,40,63,85,92,100,126,131,185,196,200,204,
%T 242,246,272,274,282,379,553,572,654,777,902,1100,1216,1225,1236,1316,
%U 1413,1658,1943,2077,2086,2744,2746,2856,2860,3518,3718,4184,4189,4363
%N When the numerator - denominator (A064169) in n-th harmonic number is prime.
%H Amiram Eldar, <a href="/A064404/b064404.txt">Table of n, a(n) for n = 1..92</a>
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=lcm(n!,1/2%2B1/3%2B1/4%2B...%2B1/n)/n!&action=Search">PRP Records</a>
%t s = 1; Do[ m = n; s = s + 1/n; If[ PrimeQ[ Numerator[ s ] - Denominator[ s ] ], Print[ n ] ], {n, 2, 2500} ]
%t hnoQ[n_]:=Module[{h=HarmonicNumber[n]},PrimeQ[Numerator[h]-Denominator[ h]]]; Select[Range[5000],hnoQ] (* _Harvey P. Dale_, May 23 2012 *)
%o (PARI) for(n=2, 300, if(isprime(lcm(n!, sum(k=2, n, 1/k))/n!), print1(n, ", "))); \\ _Arkadiusz Wesolowski_, Oct 13 2011
%Y Cf. A064169.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 28 2001
%E More terms from _Arkadiusz Wesolowski_, Oct 13 2011
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