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%I #12 Apr 19 2023 09:05:14
%S 2,3,5,11,23,47,59,167,179,239,359,719,839,1259,3359,5039,10079,35279,
%T 37799,55439,110879,166319,665279,831599,1081079,1441439,6320159,
%U 6486479,12972959,24504479,61261199,82162079,136936799,232792559,410810399,698377679,735134399
%N Primes p for which sigma(p+1)/sigma(p) reaches a record value, where sigma(k) is the divisor sum function (A000203).
%C Garcia et al. proved that {sigma(p+1)/sigma(p) : p prime} is dense in [3/2, oo), and thus this sequence is infinite.
%H Stephan Ramon Garcia, Florian Luca, Kye Shi, and Gabe Udell, <a href="https://arxiv.org/abs/1906.05927">Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function</a>, arXiv:1906.05927 [math.NT], 2019.
%e The values of sigma(p+1)/sigma(p) for the first terms are 1.333... < 1.75 < 2 < 2.333... < 2.5 < ...
%t s = {}; rm = 0; p = 2; Do[q = NextPrime[p]; r = DivisorSigma[1, p + 1]/DivisorSigma[1, p]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^3}]; s
%Y Cf. A000203, A008333.
%K nonn
%O 1,1
%A _Amiram Eldar_, Sep 11 2019
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