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%I #17 Apr 16 2024 16:01:36
%S 2,3,5,7,13,31,37,61,181,241,421,1009,1321,1801,2161,2521,6301,7561,
%T 12601,15121,20161,30241,45361,55441,100801,110881,196561,332641,
%U 498961,786241,982801,1108801,1580041,1940401,1995841,2402401,3880801,4324321,11476081,11531521
%N Primes p such that p-1 has more divisors than any smaller prime-1.
%C 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
%H David A. Corneth, <a href="/A103199/b103199.txt">Table of n, a(n) for n = 1..130</a> (first 75 terms from Amiram Eldar)
%H Karl Prachar, <a href="https://doi.org/10.1007/BF01302992">Über die Anzahl der Teiler einer natürlichen Zahl, welche die Form p-1 haben</a>, Monatshefte für Mathematik, Vol. 59 (1955), pp. 91-97.
%t 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 *)
%o (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
%Y Cf. A000005, A008328, A066814, A067573, A072826.
%K nonn
%O 1,1
%A _Don Reble_, Mar 19 2005
%E a(38)-a(40) added and name clarified by _Amiram Eldar_, Apr 16 2024
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