OFFSET
1,1
COMMENTS
If 2^p-1 is a prime (Mersenne prime) greater than 3 then 2^(p-2)*(2^p-1) is in the sequence. So for n>1, 2^(A000043(n)-2)*(2^A000043(n)-1) is in the sequence. - Farideh Firoozbakht, Feb 23 2005
Theorem: If m>0, k is an integer and p=2^(m+2)+k-1 is a prime number then n=2^m*p is a solution to the equation sigma(x) = 4*phi(x)-k. The previous comment is the special case k=0. - Farideh Firoozbakht, Oct 01 2014
REFERENCES
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 88.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..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.
Farideh Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1
MATHEMATICA
Select[Range[900000], DivisorSigma[1, #]==4EulerPhi[#]&] (* Harvey P. Dale, Nov 29 2013 *)
PROG
(PARI) for(n=1, 300000, if(sigma(n)==4*eulerphi(n), print1(n, ", ")))
(Magma) [n: n in [1..10^6] | SumOfDivisors(n) eq 4*EulerPhi(n)]; // Vincenzo Librandi, Sep 25 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 03 2002
EXTENSIONS
More terms from Carl Najafi, Aug 16 2011
STATUS
approved