A229493 Irregular triangle in which row n has numbers k such that prime(n) divides A001008(k), the numerator of the k-th harmonic number.

2, 7, 22, 4, 20, 24, 6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728, 3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888, 958, 962, 966, 1291, 1293, 9328, 9331, 9335, 9338, 9376, 9378, 10583, 10587, 10591, 14205, 14207

Offset

2,1

Comments

The length of each row is given in A092103.

Links

Table of n, a(n) for n=2..52.

David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - Max Alekseyev, Oct 23 2012]

A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.

C. Sanna, On the p-adic valuation of harmonic numbers, J. Number Theory 166 (2016), 41-46.

Example

The irregular triangle begins:
2, 7, 22
4, 20, 24
6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728
3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888,...

Mathematica

(* 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}}]]

Crossrefs

Cf. A092103 (number of k for which prime(n) divides A001008(k)).

Sequence in context: A150321 A076716 A088591 * A175871 A137107 A284921

Adjacent sequences: A229490 A229491 A229492 * A229494 A229495 A229496

Keyword

nonn,tabf

Author

T. D. Noe and Arkadiusz Wesolowski, Nov 11 2013

Status

approved