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

1,1

Comments

The prime terms are Wieferich primes.

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

Links

Table of n, a(n) for n=1..18.

PrimeGrid, Wieferich prime search - PRPNet server statistics

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

Cf. A001220, A240719.

Sequence in context: A355545 A291194 A331021 * A273471 A266829 A203858

Adjacent sequences: A270830 A270831 A270832 * A270834 A270835 A270836

Keyword

nonn

Author

Felix Fröhlich, Mar 23 2016

Status

approved