A270833 Numbers n > 1 where all prime factors are Wieferich primes, i.e., terms of A001220.

1093, 3511, 1194649, 3837523, 12327121, 1305751357, 4194412639, 13473543253, 43280521831, 1427186233201, 4584493014427, 14726582775529, 47305610361283, 151957912148641, 5010850864768711, 16096154973653197, 51705032124882319, 166089997978464613

Offset: 1

Author

Felix Fröhlich, Mar 23 2016

Keywords

• nonn

Comments

The prime terms are Wieferich primes.

All "Wieferich pseudoprimes", if any exist, are in the sequence (see second comment in A240719).

Examples

			4194412639 = 1093^2 * 3511. All prime factors are Wieferich primes, so 4194412639 is a term of the sequence.
		

Links

• PrimeGrid, Wieferich prime search - PRPNet server statistics

Crossrefs

Cf. A001220, A240719.

Programs

Mathematica

Take[#, 19] &@ Rest@ Sort@ Map[1093^First@ # 3511^Last@ # &, Tuples[Range[0, 6], 2]] (* Michael De Vlieger, Mar 24 2016 *)

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")