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Largest k such that prime(n) divides the numerator of the k-th harmonic number (=A001008(k)).
3

%I #18 Feb 19 2016 16:03:12

%S 22,24,102728,1011849771855214912968404217247,168,288,848874360,528,

%T 695552,886725671,50641,1680,2359785,10776888210,414839198,

%U 42176361744,226972,4488,9094138358932,5328,6240

%N Largest k such that prime(n) divides the numerator of the k-th harmonic number (=A001008(k)).

%C For p = prime(n), Boyd defines J_p to be the set of numbers k such that p divides A001008(k). This sequence gives the largest element of J_p. The smallest element of J_p is given by A072984. The size of J_p is given by A092103.

%C a(24)-a(26) = [704942, 73068455829392952709, 1093588833695991475]. - _Max Alekseyev_, Feb 19 2016

%H David W. Boyd, <a href="http://www.emis.de/journals/EM/expmath/volumes/3/3.html">A p-adic study of the partial sums of the harmonic series</a>, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - _Max Alekseyev_, Feb 10 2016]

%F For p = prime(n) in A092101, a(n) = p^2 - 1.

%Y Cf. A072984, A092103, A092193.

%K hard,more,nonn

%O 2,1

%A _Max Alekseyev_, May 12 2010

%E a(5) computed by Boyd.

%E a(8)-a(22) from _Max Alekseyev_, Oct 23 2012