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A068423

Numbers k such that sigma(k) = 2*phi(k+1).

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

1,1

COMMENTS

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

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..758 (terms below 10^10, terms 1..80 from Harvey P. Dale)

MAPLE

select(t -> numtheory:-sigma(t) = 2*numtheory:-phi(t+1), [$1..10^6]); # Robert Israel, Aug 14 2014

MATHEMATICA

With[{nn=250000}, Position[Thread[{DivisorSigma[1, Range[nn]], 2*EulerPhi[ Range[ 2, nn+1]]}], {x_, x_}]]//Flatten (* Harvey P. Dale, Mar 19 2016 *)

PROG

(PARI) isok(n) = sigma(n) == 2*eulerphi(n+1); \\ Michel Marcus, Nov 24 2013

CROSSREFS

Cf. A000010, A000203, A000668.

Sequence in context: A288653 A287905 A287947 * A287599 A287625 A019210