OFFSET
1,1
COMMENTS
The prime terms are Wieferich primes.
All "Wieferich pseudoprimes", if any exist, are in the sequence (see second comment in A240719).
EXAMPLE
4194412639 = 1093^2 * 3511. All prime factors are Wieferich primes, so 4194412639 is a term of the sequence.
MATHEMATICA
Take[#, 19] &@ Rest@ Sort@ Map[1093^First@ # 3511^Last@ # &, Tuples[Range[0, 6], 2]] (* Michael De Vlieger, Mar 24 2016 *)
PROG
(PARI) is(n) = if(n==1, return(0)); my(f=factor(n)[, 1]); for(k=1, #f, if(Mod(2, f[k]^2)^(f[k]-1)!=1, return(0))); return(1)
(PARI) /* The following program is significantly faster; valid up to (p^x * q^y) < b, where b is the upper search bound for Wieferich primes (approximately 5*10^17 as of Mar 23 2016, see PrimeGrid PRPNet server statistics) */
my(p=1093, q=3511, v=vector(0), w=vector(1)); for(x=0, 4, for(y=0, 4, w[1]=p^x*q^y; v=concat(v, w))); vecextract(vecsort(v, , 8), "2..25")
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Mar 23 2016
STATUS
approved