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A172314
Numbers k such that phi(k+1) = 4*phi(k).
5
1260, 13650, 17556, 18720, 24510, 42120, 113610, 244530, 266070, 712080, 749910, 795690, 992250, 1080720, 1286730, 1458270, 1849470, 2271060, 2457690, 3295380, 3370770, 3414840, 3714750, 4061970, 4736490, 5314050, 5827080, 6566910, 6935082, 7303980, 7864080
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
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