A177734 - OEIS

A177734

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

22, 24, 102728, 1011849771855214912968404217247, 168, 288, 848874360, 528, 695552, 886725671, 50641, 1680, 2359785, 10776888210, 414839198, 42176361744, 226972, 4488, 9094138358932, 5328, 6240

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OFFSET

2,1

COMMENTS

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.

a(24)-a(26) = [704942, 73068455829392952709, 1093588833695991475]. - Max Alekseyev, Feb 19 2016

LINKS

Table of n, a(n) for n=2..22.

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, Feb 10 2016]

FORMULA

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

CROSSREFS

Cf. A072984, A092103, A092193.

Sequence in context: A155911 A061411 A053779 * A177055 A186780 A034304

Adjacent sequences: A177731 A177732 A177733 * A177735 A177736 A177737

KEYWORD

hard,more,nonn

AUTHOR

Max Alekseyev, May 12 2010

EXTENSIONS

a(5) computed by Boyd.

a(8)-a(22) from Max Alekseyev, Oct 23 2012

STATUS

approved