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 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 (list; graph; refs; listen; history; text; internal format)
 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, 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

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Last modified October 17 13:20 EDT 2021. Contains 348049 sequences. (Running on oeis4.)