A295740 Even pseudoprimes (A006935) that are not squarefree.

190213279479817426, 283959621257123566, 301971651496560046, 575203724324614126, 800951203404568126, 849341919686285026, 1118572636403947726, 2080713636347910526, 2270517620327541586, 2767984602684877486, 5013069719001987826, 5133266340887464066, 5252931629341901506, 5743747078662858526

Offset: 1

Author

Max Alekseyev, Nov 26 2017

Keywords

• nonn

Comments

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.

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

Examples

			a(1) = 190213279479817426 = 2 * 7 * 79 * 1951 * 3511^2 * 7151.
a(2) = 283959621257123566 = 2 * 599 * 937 * 3511^2 * 20521.
a(3) = 301971651496560046 = 2 * 31 * 71 * 73 * 3511^2 * 76231.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..80 (5 wrong terms were removed by _Mauro Fiorentini_, May 31 2020)

Crossrefs

Intersection of A006935 and A013929.

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