OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is 0 (Dressler, 1974). - Amiram Eldar, Jul 23 2020
Conjecture: Every term is a square or twice a square. - Jason Yuen, May 16 2024
The conjecture is true: If k is neither a square nor twice a square (i.e., in A028983), then sigma(k) is even. Since gcd(phi(k), sigma(k)) = 1, then phi(k) must be odd, but phi(k) is odd only for k = 1 and 2. - Amiram Eldar, May 19 2024
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..10000
Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.
EXAMPLE
For n = 484, phi(484) = 220 = 2*2*5*11, sigma(484) = 931 = 7*7*19, and gcd(220,931) = 1.
MATHEMATICA
Select[Range@ 2700, CoprimeQ[EulerPhi@ #, DivisorSigma[1, #]] &] (* Michael De Vlieger, Feb 05 2017 *)
Select[With[{max = 51}, Union[Array[#^2 &, max], Array[2*#^2 &, Floor[max / Sqrt[2]]]]], CoprimeQ[EulerPhi[#], DivisorSigma[1, #]] &] (* Amiram Eldar, May 19 2024 *)
PROG
(PARI) is(n)=gcd(sigma(n), eulerphi(n))==1 \\ Charles R Greathouse IV, Feb 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, May 31 2000
EXTENSIONS
Incorrect comment removed by Charles R Greathouse IV, Feb 19 2013
STATUS
approved