A110073 Numbers n such that sigma(n)=2n-phi(phi(n)).

1, 2, 4, 10, 76, 410, 890, 1370, 2330, 5690, 8090, 8570, 10490, 10970, 11930, 14330, 19130, 21530, 27770, 32090, 34490, 35930, 38330, 39290, 40730, 44570, 47930, 49370, 52730, 54170, 60890, 64730, 65690, 68570, 74330, 75290, 75770, 78170

Offset

1,2

Comments

If p is an odd prime and 8p+1 is prime then n=10(8p+1) is in the sequence because 2n-phi(phi(n))=20(8p+1)-16(p-1)=144p+3618*(8p+2)=sigma(n).

Conjecture: Each term which is greater than 76 of this sequence is of the form 80p+10 where both p and 8p+1 are primes.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

76 is in the sequence because sigma(76)=2*76-phi(phi(76)).

Mathematica

Do[If[DivisorSigma[1, m] == 2m - EulerPhi[EulerPhi[m]], Print[m]], {m, 100000}]

Prog

(PARI) is(n)=sigma(n)==2*n-eulerphi(eulerphi(n)) \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Cf. A110074.

Sequence in context: A215439 A120402 A182238 * A090256 A270479 A126140

Adjacent sequences: A110070 A110071 A110072 * A110074 A110075 A110076

Keyword

nonn

Author

Farideh Firoozbakht, Jul 23 2005

Status

approved