|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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 ].
|
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|