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

Author

Seiichi Manyama, Feb 09 2019

Keywords

• nonn
• more

Comments

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

Examples

			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
		

Links

• 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.

Crossrefs

Cf. A000203, A067698, A079526, A079527.

Programs

Mathematica

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