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A323278 Numbers of the form p^2-1 that have a record-breaking number of divisors, where p is prime.

%I A323278 #41 Feb 09 2019 11:11:33
%S A323278 3,8,24,48,120,288,360,840,1680,5040,11880,32760,143640,201600,491400,
%T A323278 776160,2042040,3500640,7447440,9480240,17297280,34234200,143256960,
%U A323278 514337040,555120720,569729160,1656408600,4283571600,8148853440,10951831800,35415099720,51437786400
%N A323278 Numbers of the form p^2-1 that have a record-breaking number of divisors, where p is prime.
%C A323278 a(11)-a(26) from Chuck Gaydos.
%H A323278 Chai Wah Wu, <a href="/A323278/b323278.txt">Table of n, a(n) for n = 1..63</a>
%H A323278 Chris Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=23869">Prime Curio for 23869</a>
%e A323278 a(7) = 360 because 360 has a record-breaking 24 divisors and 360 = p^2-1, where p = 19 is prime.
%t A323278 Block[{s = Prime[Range[10^5]]^2 - 1, t}, t = DivisorSigma[0, s]; Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]] (* _Michael De Vlieger_, Jan 19 2019 *)
%o A323278 (PARI) lista(nn) = {my(m = 0, p = 2, np); for (n=1, nn, np = p^2-1; if (((nd = numdiv(np)) > m), print1(np, ", "); m = nd); p = nextprime(p+1););} \\ _Michel Marcus_, Jan 12 2019
%o A323278 (Python)
%o A323278 from sympy import divisor_count, nextprime
%o A323278 A323278_list, p, nmax = [], 2 , -1
%o A323278 while len(A323278_list) < 100:
%o A323278     n = divisor_count(p**2-1)
%o A323278     if n > nmax:
%o A323278         nmax = n
%o A323278         A323278_list.append(p**2-1)
%o A323278     p = nextprime(p) # _Chai Wah Wu_, Feb 09 2019
%Y A323278 Cf. A000005, A084920.
%K A323278 nonn
%O A323278 1,1
%A A323278 _G. L. Honaker, Jr._, Jan 11 2019
%E A323278 a(27)-a(32) from _Daniel Suteu_, Jan 12 2019