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Even pseudoprimes (A006935) that are not squarefree.
6

%I #34 May 31 2020 17:39:06

%S 190213279479817426,283959621257123566,301971651496560046,

%T 575203724324614126,800951203404568126,849341919686285026,

%U 1118572636403947726,2080713636347910526,2270517620327541586,2767984602684877486,5013069719001987826,5133266340887464066,5252931629341901506,5743747078662858526

%N Even pseudoprimes (A006935) that are not squarefree.

%C For a prime p, if p^2 divides an even pseudoprime, then p is a Wieferich prime (A001220) and A007733(p)=A002326((p-1)/2) is odd. Currently, the only known such prime is p=3511.

%C So, all known terms are multiples of 3511^2. Furthermore, no term can be a multiple of 3511^3.

%H Max Alekseyev, <a href="/A295740/b295740.txt">Table of n, a(n) for n = 1..80</a> (5 wrong terms were removed by _Mauro Fiorentini_, May 31 2020)

%e a(1) = 190213279479817426 = 2 * 7 * 79 * 1951 * 3511^2 * 7151.

%e a(2) = 283959621257123566 = 2 * 599 * 937 * 3511^2 * 20521.

%e a(3) = 301971651496560046 = 2 * 31 * 71 * 73 * 3511^2 * 76231.

%Y Intersection of A006935 and A013929.

%Y The even terms of A158358. Also, unless there is a Wieferich prime greater than 3511, the even terms of A247831.

%K nonn

%O 1,1

%A _Max Alekseyev_, Nov 26 2017