

A197112


Numbers n such that phi(n) = phi(n+1) + phi(n+2).


1



193, 3529, 9337, 27229, 46793, 78181, 90193, 112993, 135013, 437183, 849403, 935219, 1078579, 1283599, 1986973, 2209583, 2341183, 2411173, 2689693, 2744143, 3619069, 3712543, 4738183, 5132983, 6596119, 7829029, 8184713
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OFFSET

1,1


COMMENTS

For n less than 4*10^6, n is prime, semiprime, or triprime (3almost prime).


LINKS

Table of n, a(n) for n=1..27.


FORMULA

a(n) = A066232(n)2.  Donovan Johnson, Oct 14 2011


EXAMPLE

112993 is in the sequence, because phi(112993)=106704, phi(112994)=48384, phi(112995)=58320 and 106704=48384+58320.


MAPLE

for k from 0 do
if numtheory[phi](k) = numtheory[phi](k+1)+numtheory[phi](k+2) then
printf("%d\n", k) ;
end if;
end do: # R. J. Mathar, Oct 13 2011


MATHEMATICA

Select[Range[10^5], EulerPhi[#] == EulerPhi[# + 1] + EulerPhi[# + 2] &] (* Alonso del Arte, Oct 13 2011 *)


PROG

(PARI) isok(n) = eulerphi(n) == eulerphi(n+1) + eulerphi(n+2); \\ Michel Marcus, May 15 2016


CROSSREFS

Cf. A092404.
Sequence in context: A178265 A201112 A250156 * A120851 A302332 A198483
Adjacent sequences: A197109 A197110 A197111 * A197113 A197114 A197115


KEYWORD

nonn


AUTHOR

Antonio Roldán, Oct 10 2011


EXTENSIONS

a(27) from Vincenzo Librandi, Sep 27 2013


STATUS

approved



