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A278836
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Numbers n such that 2^n == 1 (mod sigma(n)).
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2
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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
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1,2
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COMMENTS
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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)
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LINKS
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EXAMPLE
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8 is a term because sigma(8) = 15 divides 2^8 - 1.
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MAPLE
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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
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MATHEMATICA
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{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 *)
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PROG
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(PARI) is(n)=Mod(2, sigma(n))^n==1;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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