A246803 Solutions of phi(sigma(x)) = x-phi(x).

6, 10, 14, 20, 22, 24, 34, 40, 44, 46, 56, 62, 68, 88, 92, 94, 106, 136, 142, 152, 164, 184, 188, 212, 214, 232, 248, 254, 284, 332, 376, 382, 384, 424, 428, 464, 472, 568, 632, 640, 668, 712, 764, 766, 856, 862, 864, 896, 944, 1004, 1016, 1172, 1192, 1294, 1408, 1424, 1432

Offset

1,1

Comments

For n>1, 2*A005105(n) is in the sequence.

So is 8*A005105(n). 4*A005105(n) is in the sequence if A005105(n) == 5 mod 6 (i.e., is not 2 or in A000668). - Robert Israel, Oct 01 2014

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Example

20 is in the sequence since phi(sigma(20)) = phi(42) = 12 = 20-phi(20).

Maple

with(numtheory): A246803:=n->`if`(phi(sigma(n)) = n-phi(n), n, NULL): seq(A246803(n), n=1..2000); # Wesley Ivan Hurt, Sep 30 2014

Mathematica

Select[Range[1500], EulerPhi[DivisorSigma[1, #]]==#-EulerPhi[#]&]

Prog

(PARI) is(k) = {my(f = factor(k)); eulerphi(sigma(f)) == k - eulerphi(f); } \\ Amiram Eldar, Nov 10 2024

Crossrefs

Cf. A000010, A000203, A000668, A005105.

Sequence in context: A315197 A315198 A006617 * A140695 A085681 A315199

Adjacent sequences: A246800 A246801 A246802 * A246804 A246805 A246806

Keyword

nonn

Author

Jahangeer Kholdi, Sep 28 2014

Status

approved