A295740 Even pseudoprimes (A006935) that are not squarefree.

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

Offset

1,1

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.

Links

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

Example

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.

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.

Sequence in context: A261152 A292634 A308287 * A270271 A094676 A327760

Adjacent sequences: A295737 A295738 A295739 * A295741 A295742 A295743

Keyword

nonn

Author

Max Alekseyev, Nov 26 2017

Status

approved