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%I #42 Sep 18 2023 06:18:40
%S 2,4,11,29,131,419,1429,14629,77141,509081,1456729,22486309,117048931,
%T 1625292241,10326137821,117440297701,1110819807371,8678298841211,
%U 138645880242871,980010587880169
%N Smallest number k such that k^2 - 1 has exactly n distinct prime factors.
%C a(14) <= 1625292241. - _Donovan Johnson_, Nov 10 2012
%H Michael S. Branicky, <a href="/A219017/a219017.py.txt">Python program</a>
%e a(3) = 11 is the smallest number of the set {k(i)} = {11, 13, 14, 16, 19, 20, ...} where k(i)^2 - 1 contains 3 distinct prime factors.
%e a(10) = 509081 because 509081^2-1 = 2 ^ 4 * 3 * 5 * 7 * 11 * 13 * 17 * 23 * 31 * 89 with 10 distinct prime factors.
%p with(numtheory) :for n from 1 to 11 do:ii:=0:for k from 1 to 10^10 while(ii=0) do:x:=k^2-1:y:=factorset(x):n1:=nops(y):if n1=n then ii:=1: printf ( "%d %d \n",n,k):
%p else fi:od:od:
%t L = {}; Do[n = 2; While[Length[FactorInteger[n^2 - 1]] != k, n++]; Print@AppendTo[L, n], {k, 15}] (* _Giovanni Resta_, Nov 10 2012 *)
%Y Cf. A180278.
%K nonn,hard,more
%O 1,1
%A _Michel Lagneau_, Nov 09 2012
%E a(12)-a(13) from _Donovan Johnson_, Nov 10 2012
%E a(14)-a(17) from _Giovanni Resta_, May 10 2017
%E a(18) from _Michael S. Branicky_, Feb 08 2023
%E a(19) from _Michael S. Branicky_, Feb 15 2023
%E a(20) from _Michael S. Branicky_, Feb 19 2023
%E Name clarified by _Pontus von Brömssen_, Sep 12 2023
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