A267487 Primes p such that A001221(p+1)^(p-1) == 1 (mod p^2).

2, 3, 7, 31, 127, 1093, 3511, 8191, 131071, 524287

Offset: 1

Author

Felix Fröhlich, Jan 15 2016

Keywords

• nonn
• more

Comments

No further terms up to 10^9.

Are all terms of A000668 and A001220 in the sequence?

Does the sequence contain any terms not in A000668 or A001220 other than 2?

Crossrefs

Cf. A000668, A001220, A260377.

Programs

Maple

isA267487 := proc(p)
    if isprime(p) then
        A001221(p+1) ;
        simplify(modp(% &^ (p-1),p^2) =1 );
    else
        false;
    end if;
end proc:
p := 2;
for i from 1 do
    if isA267487(p) then
        printf("%d\n",p) ;
    end if;
    p := nextprime(p) ;
end do: # R. J. Mathar, Jan 23 2016

Mathematica

Select[Prime[Range[3200]], Mod[PrimeNu[# + 1], #^2]^(# - 1) == 1 &] (* G. C. Greubel, Apr 25 2017 *)

PARI

forprime(p=1, 1e9, if(Mod(omega(p+1), p^2)^(p-1)==1, print1(p, ", ")))