

A278836


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


2



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
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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



