A335325 Primes p such that d(p^2-1) sets a record, where d(n) is the number of divisors of n.

2, 3, 5, 7, 11, 17, 19, 29, 41, 71, 109, 181, 379, 449, 701, 881, 1429, 1871, 2729, 3079, 4159, 5851, 11969, 22679, 23561, 23869, 40699, 65449, 90271, 104651, 188189, 226799, 244529, 252449, 388961, 403649, 815671, 825551, 1276001, 2380951, 2408561

Offset: 1

Author

Austin Nguyen Tran, May 31 2020

Keywords

• nonn

Examples

			7^2-1 = 48 has 10 factors, which is the largest for any prime <= 7 (5^2-1 has 8 factors, 3^2-1 has 4 factors, and 2^2-1 has 2 factors).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A000005, A341655.

Programs

Mathematica

seq[len_] := Module[{s = {}, p = 2, dm = 0, c = 0, d}, While[c < len, If[(d = DivisorSigma[0, p^2 - 1]) > dm, dm = d; c++; AppendTo[s, p]]; p = NextPrime[p]]; s]; seq[30] (* Amiram Eldar, Jul 07 2022 *)

PARI

my(r=0,d);forprime(p=2,3*10^6,if((d=numdiv(p^2-1))>r,r=d;print1(p,", "))); \\ Joerg Arndt, Jun 01 2020