OFFSET
1,1
COMMENTS
Up to 5*10^12 only n=696004 satisfies the similar relation phi(n)/sigma(n)=phi(n-1)/sigma(n-1), or equivalently, phi(n)sigma(n-1)=phi(n-1)/sigma(n). - Giovanni Resta, Aug 05 2013
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 136, pp 46, Ellipses, Paris 2008.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..52 (terms < 10^13)
EXAMPLE
124 is in the sequence because phi(124)*sigma(124) = 60*224 = 13440 and phi(123)*sigma(123) = 80*168 = 13440, so that we indeed have phi(124)*sigma(124) = phi(123)*sigma(123).
MAPLE
lastv:= 0: A:= NULL:
for n from 1 to 10^7 do
v:= numtheory:-phi(n)*numtheory:-sigma(n);
if v = lastv then A:= A, n fi;
lastv:= v;
od:
A; # Robert Israel, Feb 04 2018
MATHEMATICA
Select[Range[10^7], EulerPhi[#]DivisorSigma[1, #] == EulerPhi[# - 1] DivisorSigma[1, # - 1] &] (* Vincenzo Librandi, Feb 05 2018 *)
PROG
(PARI) isok(n) = (eulerphi(n)*sigma(n) == eulerphi(n-1)*sigma(n-1)) \\ Michel Marcus, Jul 28 2013
(Magma) [n: n in [2..10^6] | (EulerPhi(n)*SumOfDivisors(n) eq EulerPhi(n-1)*SumOfDivisors(n-1))]; // Vincenzo Librandi, Feb 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jul 14 2008
EXTENSIONS
a(29)-a(33) from Donovan Johnson, Jul 25 2011
Duplicated entry (19305) deleted by Giovanni Resta, Aug 05 2013
STATUS
approved