A292562 Odd numbers n such that 2^d(n) == 2^n (mod n) where d = A000005.

1, 9, 19313, 226703, 345023, 673663, 929783, 1697609, 1790159, 1878073, 2391991, 3441743, 8026103, 9520441, 9770153, 10751841, 30652223, 35482433, 40642103, 41839231, 50358247, 57233047, 65046479, 69601193, 85246441, 110944089, 117368839, 119611073, 122527433

Offset

1,2

Comments

Square terms are 1, 3^2, 3^2*1093^2, 3^2*3511^2 and there are no other squares k^2 with k < 3*10^9. Note that 1093 and 3511 are Wieferich primes (A001220). - Giovanni Resta, Sep 19 2017

Links

Table of n, a(n) for n=1..29.

Example

19313 = 7*31*89 is a term because d(19313) = 2^3 and 7*31*89 divides 2^(7*31*89) - 2^8.

Mathematica

Select[Range[1, 10^7, 2], PowerMod[2, DivisorSigma[0, #], #] == PowerMod[2, #, #] &] (* Michael De Vlieger, Sep 19 2017 *)

Prog

(PARI) isok(n) = n%2==1 && Mod(2, n)^n==2^numdiv(n);

Crossrefs

Cf. A000005.

Sequence in context: A360762 A206461 A258719 * A140596 A280900 A333554

Adjacent sequences: A292559 A292560 A292561 * A292563 A292564 A292565

Keyword

nonn

Author

Altug Alkan, Sep 19 2017

Status

approved