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A064404

When the numerator - denominator (A064169) in n-th harmonic number is prime.

3, 4, 6, 7, 10, 19, 20, 26, 30, 31, 33, 40, 63, 85, 92, 100, 126, 131, 185, 196, 200, 204, 242, 246, 272, 274, 282, 379, 553, 572, 654, 777, 902, 1100, 1216, 1225, 1236, 1316, 1413, 1658, 1943, 2077, 2086, 2744, 2746, 2856, 2860, 3518, 3718, 4184, 4189, 4363

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..92

Henri Lifchitz and Renaud Lifchitz, PRP Records

MATHEMATICA

s = 1; Do[ m = n; s = s + 1/n; If[ PrimeQ[ Numerator[ s ] - Denominator[ s ] ], Print[ n ] ], {n, 2, 2500} ]

hnoQ[n_]:=Module[{h=HarmonicNumber[n]}, PrimeQ[Numerator[h]-Denominator[ h]]]; Select[Range[5000], hnoQ] (* Harvey P. Dale, May 23 2012 *)

PROG

(PARI) for(n=2, 300, if(isprime(lcm(n!, sum(k=2, n, 1/k))/n!), print1(n, ", "))); \\ Arkadiusz Wesolowski, Oct 13 2011

CROSSREFS