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A103199
Primes p such that p-1 has more divisors than any smaller prime-1.
3
2, 3, 5, 7, 13, 31, 37, 61, 181, 241, 421, 1009, 1321, 1801, 2161, 2521, 6301, 7561, 12601, 15121, 20161, 30241, 45361, 55441, 100801, 110881, 196561, 332641, 498961, 786241, 982801, 1108801, 1580041, 1940401, 1995841, 2402401, 3880801, 4324321, 11476081, 11531521
OFFSET
1,1
COMMENTS
There are infinitely many primes p such that d(p-1) > exp(c*log(p)/log(log(p))), where d(k) is the number of divisors of k, and c > 0 is a constant (Prachar, 1955). Therefore, this sequence is infinite. - Amiram Eldar, Apr 16 2024
LINKS
David A. Corneth, Table of n, a(n) for n = 1..130 (first 75 terms from Amiram Eldar)
Karl Prachar, Über die Anzahl der Teiler einer natürlichen Zahl, welche die Form p-1 haben, Monatshefte für Mathematik, Vol. 59 (1955), pp. 91-97.
MATHEMATICA
seq[pmax_] := Module[{d, dm = 0, s = {}, p = 1}, While[p < pmax, p = NextPrime[p]; d = DivisorSigma[0, p-1]; If[d > dm, dm = d; AppendTo[s, p]]]; s]; seq[10^6] (* Amiram Eldar, Apr 16 2024 *)
PROG
(PARI) lista(pmax) = {my(dm = 0, d); forprime(p = 1, pmax, d = numdiv(p-1); if(d > dm, dm = d; print1(p, ", "))); } \\ Amiram Eldar, Apr 16 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Don Reble, Mar 19 2005
EXTENSIONS
a(38)-a(40) added and name clarified by Amiram Eldar, Apr 16 2024
STATUS
approved