A376848 Numbers k such that phi(k + phi(k)) = phi(k) + phi(phi(k)), where phi = A000010.

2, 5, 9, 10, 14, 18, 20, 27, 28, 36, 38, 40, 46, 54, 56, 72, 76, 78, 80, 81, 92, 108, 112, 144, 152, 156, 160, 162, 184, 216, 224, 234, 243, 258, 288, 294, 304, 312, 320, 324, 368, 432, 438, 448, 468, 486, 516, 526, 570, 576, 588, 608, 609, 624, 640, 648, 702, 718, 729, 736, 754, 774, 864, 876

Offset: 1

Author

Robert Israel, Oct 06 2024

Keywords

• nonn

Comments

If k is in A126955, then 8*k + 6 is a term.

Examples

			a(4) = 10 is a term because phi(10) = 4, phi(4) = 2, and phi(10 + 4) = phi(14) = 6 = 4 + 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A126955, A376830, A376831, A376843, A376844, A376849, A376851.

Programs

Maple

filter:= proc(k) uses numtheory; local s;
 s:= phi(k);
 phi(k+s) = s + phi(s)
end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range[880], EulerPhi[ #+EulerPhi[#]]==EulerPhi[#]+EulerPhi[EulerPhi[#]] &] (* Stefano Spezia, Oct 07 2024 *)