A326391 Lesser of twin primes p >= 3 for which sigma(p+1)/sigma(p-1) reaches record value, where sigma(n) is the divisor sum function (A000203).

3, 7559, 42839, 55439, 110879, 415799, 1713599, 1940399, 2489759, 6652799, 6846839, 15855839, 31600799, 85765679, 232792559, 845404559, 1470268799, 6299092799, 10708457759, 17459441999, 32125373279, 135019684799, 439977938399, 449755225919, 1799020903679, 2126560035599, 2835413380799, 6278415343199

Offset

1,1

Comments

Garcia et al. proved that assuming Dickson's conjecture, {sigma(p+1)/sigma(p-1) : p and p+2 are prime} is dense in [0, oo), and thus this sequence is infinite.

Links

Table of n, a(n) for n=1..28.

Stephan Ramon Garcia, Florian Luca, Kye Shi, Gabe Udell, Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function, arXiv:1906.05927 [math.NT], 2019.

Wikipedia, Dickson's conjecture.

Example

The values of sigma(p+1)/sigma(p-1) for the first terms are 2.333... < 2.539... < 2.621... < 2.734... < 2.836...

Mathematica

s = {}; rm = 0; p = 2; Do[q = NextPrime[p]; If[q - p != 2, p = q; Continue[]]; r = DivisorSigma[1, p + 1]/DivisorSigma[1, p - 1]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^6}]; s

Crossrefs

Cf. A000203, A001359, A006512, A008332, A008333, A326356.

Sequence in context: A134776 A062595 A128147 * A068918 A356645 A362124

Adjacent sequences: A326388 A326389 A326390 * A326392 A326393 A326394

Keyword

nonn

Author

Amiram Eldar, Sep 11 2019

Extensions

a(22)-a(28) from Giovanni Resta, Nov 01 2019

Status

approved