A197112 Numbers k such that phi(k) = phi(k+1) + phi(k+2).

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

Offset: 1

Author

Antonio Roldán, Oct 10 2011

Keywords

• nonn

Comments

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..289 (calculated using the b-file at A066232)

Crossrefs

Cf. A000010, A066232, A092404.

Programs

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 *)
Position[Partition[EulerPhi[Range[82*10^5]],3,1],?(#[[1]]==#[[2]]+#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 10 2022 *)

PARI

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

Formula

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

Extensions

a(27) from Vincenzo Librandi, Sep 27 2013