cp's OEIS Frontend

A353076 Odd positive integers k such that sigma(k) > exp(gamma) * k * log(log(k))/2.

%I A353076 #18 Apr 23 2022 09:40:41
%S A353076 3,5,7,9,11,13,15,17,19,21,23,25,27,33,35,39,45,51,55,57,63,65,69,75,
%T A353076 81,87,93,99,105,117,135,147,153,165,171,189,195,207,225,231,255,273,
%U A353076 285,297,315,345,351,357,375,399,405,435,441,465,495,525,555,567,585
%N A353076 Odd positive integers k such that sigma(k) > exp(gamma) * k * log(log(k))/2.
%C A353076 The first 23 oddly colossally abundant numbers (A110464) are in this sequence.
%C A353076 According to a proof by Washington and Yang (2021), the Riemann hypothesis is equivalent to the statement that all the terms of this sequence are smaller than A110464(24) = 18565284664427130919514350125.
%H A353076 Amiram Eldar, <a href="/A353076/b353076.txt">Table of n, a(n) for n = 1..470</a>
%H A353076 Lawrence C. Washington and Ambrose Yang, <a href="https://doi.org/10.1142/S1793042121500111">Analogues of the Robin-Lagarias criteria for the Riemann hypothesis</a>, International Journal of Number Theory, Vol. 17, No. 4 (2021), pp. 843-870; <a href="https://arxiv.org/abs/2008.04787">arXiv preprint</a>, arXiv:2008.04787 [math.NT], 2020.
%e A353076 3 is in the sequence since 3 is odd and sigma(3) = 4 > exp(gamma) * 3 * log(log(3))/2 = 0.251... .
%t A353076 Select[Range[3, 600, 2], DivisorSigma[1, #] > Exp[EulerGamma] * # * Log[Log[#]]/2 &]
%o A353076 (Python) from sympy import divisor_sigma, EulerGamma, E, log
%o A353076 print([k for k in range(3, 600, 2) if divisor_sigma(k) > (E**EulerGamma * k * log(log(k)) / 2)]) # _Karl-Heinz Hofmann_, Apr 22 2022
%Y A353076 Cf. A000203 (sigma), A067698, A073004 (exp(gamma)), A110464.
%K A353076 nonn
%O A353076 1,1
%A A353076 _Amiram Eldar_, Apr 22 2022