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%I #9 Nov 10 2020 05:31:04
%S 2,7,22,4,20,24,6,42,48,295,299,337,341,2096,2390,14675,16731,16735,
%T 102728,3,7,10,77,80,84,87,110,113,117,120,848,852,856,882,888,958,
%U 962,966,1291,1293,9328,9331,9335,9338,9376,9378,10583,10587,10591,14205,14207
%N Irregular triangle in which row n has numbers k such that prime(n) divides A001008(k), the numerator of the k-th harmonic number.
%C The length of each row is given in A092103.
%H David W. Boyd, <a href="http://projecteuclid.org/euclid.em/1048515811">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_, Oct 23 2012]
%H A. Eswarathasan and E. Levine, <a href="http://dx.doi.org/10.1016/0012-365X(90)90234-9">p-integral harmonic sums</a>, Discrete Math. 91 (1991), 249-257.
%H C. Sanna, <a href="http://dx.doi.org/10.1016/j.jnt.2016.02.020">On the p-adic valuation of harmonic numbers</a>, J. Number Theory 166 (2016), 41-46.
%e The irregular triangle begins:
%e 2, 7, 22
%e 4, 20, 24
%e 6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728
%e 3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888,...
%t (* rows 2, 3, and part of 4 *) h = ParallelTable[Numerator[HarmonicNumber[i]], {i, 10000}]; Flatten[Table[Position[h, _?(Mod[#, p] == 0 &)], {p, {3, 5, 7}}]]
%Y Cf. A092103 (number of k for which prime(n) divides A001008(k)).
%K nonn,tabf
%O 2,1
%A _T. D. Noe_ and _Arkadiusz Wesolowski_, Nov 11 2013
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