A326393 Primes p for which sigma(p+1)/sigma(p) reaches a record value, where sigma(k) is the divisor sum function (A000203).

2, 3, 5, 11, 23, 47, 59, 167, 179, 239, 359, 719, 839, 1259, 3359, 5039, 10079, 35279, 37799, 55439, 110879, 166319, 665279, 831599, 1081079, 1441439, 6320159, 6486479, 12972959, 24504479, 61261199, 82162079, 136936799, 232792559, 410810399, 698377679, 735134399

Offset

1,1

Comments

Garcia et al. proved that {sigma(p+1)/sigma(p) : p prime} is dense in [3/2, oo), and thus this sequence is infinite.

Links

Table of n, a(n) for n=1..37.

Stephan Ramon Garcia, Florian Luca, Kye Shi, and 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.

Example

The values of sigma(p+1)/sigma(p) for the first terms are 1.333... < 1.75 < 2 < 2.333... < 2.5 < ...

Mathematica

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

Crossrefs

Cf. A000203, A008333.

Sequence in context: A237810 A073434 A109551 * A162278 A173927 A027763

Adjacent sequences: A326390 A326391 A326392 * A326394 A326395 A326396

Keyword

nonn

Author

Amiram Eldar, Sep 11 2019

Status

approved