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A068423
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Numbers k such that sigma(k) = 2*phi(k+1).
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1
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3, 6, 7, 28, 31, 94, 127, 322, 406, 1990, 2488, 3154, 4402, 7258, 8191, 12466, 13114, 14146, 25870, 29116, 31456, 36442, 43030, 46606, 61132, 64354, 65248, 67252, 76456, 86332, 88066, 97990, 105592, 131071, 133870, 136090, 176170, 244306
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OFFSET
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1,1
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COMMENTS
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All Mersenne primes are in the sequence. Because if p=2^q-1 is prime then 2*phi(p+1)=2*phi(2^q)=2^q=p+1=sigma(p). There are no other prime terms. - Farideh Firoozbakht, Aug 14 2014
No terms beyond a(80) up to n = 5 million. - Harvey P. Dale, Mar 19 2016
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LINKS
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MAPLE
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select(t -> numtheory:-sigma(t) = 2*numtheory:-phi(t+1), [$1..10^6]); # Robert Israel, Aug 14 2014
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MATHEMATICA
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With[{nn=250000}, Position[Thread[{DivisorSigma[1, Range[nn]], 2*EulerPhi[ Range[ 2, nn+1]]}], {x_, x_}]]//Flatten (* Harvey P. Dale, Mar 19 2016 *)
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PROG
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(PARI) isok(n) = sigma(n) == 2*eulerphi(n+1); \\ Michel Marcus, Nov 24 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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