A326392 Lesser of twin primes p for which sigma(p+1)/sigma(p) reaches record value, where sigma(n) is the divisor sum function (A000203).

3, 5, 11, 29, 59, 179, 239, 419, 1319, 3119, 3359, 7559, 21839, 35279, 42839, 55439, 110879, 415799, 1713599, 1867319, 1912679, 1940399, 2489759, 3991679, 6652799, 6846839, 11531519, 28828799, 85765679, 232792559, 845404559, 1470268799, 6285399119, 6299092799

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..34.

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) for the first terms are 1.75 < 2 < 2.333 < 2.4 < 2.8 < ...

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]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^3}]; s

Crossrefs

Cf. A000203, A001359, A006512, A008333.

Sequence in context: A046134 A177932 A328329 * A213210 A279674 A194563

Adjacent sequences: A326389 A326390 A326391 * A326393 A326394 A326395

Keyword

nonn

Author

Amiram Eldar, Sep 11 2019

Status

approved