OFFSET
1,1
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 51, p. 19, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems Number Theory, Sect. B36.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..300
V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.
M. Lal and P. Gillard, On the equation phi(n) = phi(n+k), Math. Comp. 26 (1972), 579-583.
K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. De Pauw University, 1972. [ Cf. Review on Math. Comp., Vol. 27, p. 447, 1973 ].
L. Moser, Some equations involving Euler's totient function, Amer. Math. Monthly, 56 (1949), 22-23.
A. Shinzel, Sur l'équation phi(x+k) = phi(x), Acta Arith. 4 (1958), 181-184, [MR0106857]
EXAMPLE
phi(1260) = 288. phi(1261) = 1152. 4*phi(1260) = phi(1261).
MAPLE
with(numtheory): for n from 1 to 4000000 do; if 4*phi(n) = phi(n+1) then print(n); else fi ; od;
MATHEMATICA
#[[1, 1]]&/@Select[Partition[Table[{n, EulerPhi[n]}, {n, 4000000}], 2, 1], 4#[[1, 2]]==#[[2, 2]]&] (* Harvey P. Dale, Oct 11 2011 *)
Select[Range@1000000, EulerPhi@# 4 == EulerPhi[# + 1] &] (* Vincenzo Librandi, Jan 27 2016 *)
PROG
(Magma) [n: n in [1..2*10^6] | EulerPhi(n+1) eq 4*EulerPhi(n)]; // Vincenzo Librandi, Jan 27 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 31 2010
EXTENSIONS
References separated by R. J. Mathar, Feb 19 2010
STATUS
approved