A306348 Numbers k such that exp(H_k)*log(H_k) <= sigma(k), where H_k is the harmonic number.

1, 2, 3, 4, 6, 12, 24, 60

Offset

1,2

Comments

If the Riemann hypothesis is true, there are no more terms.

Links

Table of n, a(n) for n=1..8.

J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.

Example

Let b(n) = exp(H_{a(n)})*log(H_{a(n)}).
n | a(n) |    b(n)    | sigma(a(n))
--+------+------------+-------------
1 |   1  |   0        |      1
2 |   2  |   1.817... |      3
3 |   3  |   3.791... |      4
4 |   4  |   5.894... |      7
5 |   6  |  10.384... |     12
6 |  12  |  25.218... |     28
7 |  24  |  57.981... |     60
8 |  60  | 166.296... |    168

Mathematica

For[k = 1, True, k++, If[Exp[HarmonicNumber[k]] Log[HarmonicNumber[k]] <= DivisorSigma[1, k], Print[k]]] (* Jean-François Alcover, Feb 14 2019 *)

Crossrefs

Cf. A000203, A067698, A079526, A079527.

Sequence in context: A018369 A324178 A214570 * A363670 A078495 A161701

Adjacent sequences: A306345 A306346 A306347 * A306349 A306350 A306351

Keyword

nonn,more

Author

Seiichi Manyama, Feb 09 2019

Status

approved