cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A306348 #29 Feb 14 2019 10:06:45
%S A306348 1,2,3,4,6,12,24,60
%N A306348 Numbers k such that exp(H_k)*log(H_k) <= sigma(k), where H_k is the harmonic number.
%C A306348 If the Riemann hypothesis is true, there are no more terms.
%H A306348 J. C. Lagarias, <a href="https://arxiv.org/abs/math/0008177">An elementary problem equivalent to the Riemann hypothesis</a>, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.
%e A306348 Let b(n) = exp(H_{a(n)})*log(H_{a(n)}).
%e A306348 n | a(n) |    b(n)    | sigma(a(n))
%e A306348 --+------+------------+-------------
%e A306348 1 |   1  |   0        |      1
%e A306348 2 |   2  |   1.817... |      3
%e A306348 3 |   3  |   3.791... |      4
%e A306348 4 |   4  |   5.894... |      7
%e A306348 5 |   6  |  10.384... |     12
%e A306348 6 |  12  |  25.218... |     28
%e A306348 7 |  24  |  57.981... |     60
%e A306348 8 |  60  | 166.296... |    168
%t A306348 For[k = 1, True, k++, If[Exp[HarmonicNumber[k]] Log[HarmonicNumber[k]] <= DivisorSigma[1, k], Print[k]]] (* _Jean-François Alcover_, Feb 14 2019 *)
%Y A306348 Cf. A000203, A067698, A079526, A079527.
%K A306348 nonn,more
%O A306348 1,2
%A A306348 _Seiichi Manyama_, Feb 09 2019