A278836 Numbers n such that 2^n == 1 (mod sigma(n)).

1, 2, 8, 25, 36, 50, 72, 128, 200, 288, 900, 1152, 1764, 1800, 2304, 3200, 3528, 7200, 8712, 10404, 14112, 20808, 27848, 28224, 28800, 32768, 44100, 56448, 57600, 83232, 88200, 112896, 125316, 139392, 152100, 181476, 217800, 250632, 260100, 294912, 304200, 332928, 352800, 362952, 445568

Offset

1,2

Comments

From Robert Israel, Dec 08 2016: (Start)

2^k is in the sequence if and only if k+1 is a power of 2.

If k and m are in the sequence with gcd(k,m) = 1 and gcd(sigma(k),sigma(m)) = 1, then k*m is in the sequence. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..1143

Example

8 is a term because sigma(8) = 15 divides 2^8 - 1.

Maple

N:= 10^7: # to get all terms <= N
cands:= [seq(x^2, x=1..floor(sqrt(N))), seq(2*x^2, x=1..floor(sqrt(N/2)))]:
sort(select(n -> 2 &^n -1 mod numtheory:-sigma(n) = 0, cands)); # Robert Israel, Dec 08 2016

Mathematica

{1}~Join~Select[Range[5*10^5], Mod[2^#, DivisorSigma[1, #]] == 1 &] (* Michael De Vlieger, Dec 10 2016 *)
Join[{1}, Select[Range[450000], PowerMod[2, #, DivisorSigma[1, #]]==1&]] (* Harvey P. Dale, May 14 2019 *)

Prog

(PARI) is(n)=Mod(2, sigma(n))^n==1;

Crossrefs

Cf. A000203, A000225, A279039. Contains A058891. Contained in A028982.

Sequence in context: A009515 A309088 A070944 * A227447 A077167 A062450

Adjacent sequences: A278833 A278834 A278835 * A278837 A278838 A278839

Keyword

nonn

Author

Altug Alkan, Dec 06 2016, following a suggestion from Michel Marcus

Status

approved