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A062699 Numbers n such that sigma(n) = 2*phi(n). 20
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 (list; graph; refs; listen; history; text; internal format)
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

Harry J. Smith and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 50 terms from Harry J. Smith)

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.

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.

Sequence in context: A231644 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

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Last modified May 21 22:24 EDT 2019. Contains 323467 sequences. (Running on oeis4.)