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

Author

Jason Earls, Jul 11 2001

Keywords

• nonn

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)<=nFarideh 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.

Crossrefs

Cf. A068390, A104900, A104901.

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

Programs

Mathematica

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

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

Extensions

More terms from Labos Elemer, Nov 23 2001