A062699 Numbers n such that sigma(n) = 2*phi(n).

3, 35, 1045, 24871, 29029, 50065, 58435, 64285, 87685, 137885, 140335, 1390753, 1529983, 1739507, 2011009, 2086903, 3189625, 3281663, 3501605, 3722875, 3830827, 3852155, 6605945, 7711405, 8409305, 9815195, 11413205, 11569805, 13321295, 13932919, 16540205

Offset

1,1

Comments

3 is the only prime term of this sequence. There is no term of the form p^k where p is a prime and k>1. All terms are odd because if n is even then 2*phi(n)=phi(2n)<=n<sigma(n). - Farideh Firoozbakht, Apr 01 2005, Feb 24 2007

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..50 from Harry J. Smith, terms 51..1000 from Donovan Johnson)

Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.

Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.

Mathematica

Select[Range[10^6], DivisorSigma[1, #] == 2 * EulerPhi[#] &] (* Amiram Eldar, Dec 04 2019 *)

Prog

(PARI) for(n=1, 500000, if(sigma(n)==eulerphi(n)*2, print(n)))
(PARI) n=0; for (m=1, 10^9, if(sigma(m)==2*eulerphi(m), write("b062699.txt", n++, " ", m); if (n==50, break)) ) \\ Harry J. Smith, Aug 09 2009
(PARI) is(n)=my(f=factor(n)); sigma(f)==2*eulerphi(f) \\ Charles R Greathouse IV, Aug 13 2015

Crossrefs

Cf. A068390, A104900, A104901.

Subsequence of A028983 (sigma(k) is even).

Sequence in context: A368389 A287405 A107712 * A012767 A279377 A215582

Adjacent sequences: A062696 A062697 A062698 * A062700 A062701 A062702

Keyword

nonn

Author

Jason Earls, Jul 11 2001

Extensions

More terms from Labos Elemer, Nov 23 2001

Status

approved