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
Keywords
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
Programs
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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