A283808 Numbers k such that phi(phi(k)) divides k, where phi(k) is A000010(k).

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 24, 28, 32, 36, 40, 48, 54, 56, 64, 72, 80, 96, 108, 112, 128, 144, 160, 162, 192, 216, 224, 256, 288, 320, 324, 384, 432, 448, 486, 512, 576, 640, 648, 768, 864, 896, 972, 1024, 1152, 1280, 1296, 1458, 1536, 1728, 1792, 1944, 2048, 2304, 2560

Offset

1,2

Comments

M. Hausman has proved (see Links) that a number belongs to this sequence if and only if it is of one of the following forms: 2^s, 2^s * 3^t, 5 * 2^t, or 7 * 2^t , where s >= 0 and t >= 1.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

M. Hausman, The solution of a special arithmetic equation, Canad. Math. Bull, 1982, 25(1), 114-117.

Example

56 is in the sequence because phi(phi(56)) = 8 divides 56.

Mathematica

Select[Range[1000], Mod[#, EulerPhi@ EulerPhi@ #] == 0 &]

Prog

(PARI) alias(e, eulerphi);
for(n = 1, 1000, if(!Mod(n, e(e(n))), print1(n, ", "))) \\ Indranil Ghosh, Mar 18 2017
(Python)
from sympy import totient as e
print([n for n in range(1, 1001) if n%e(e(n))==0]) # Indranil Ghosh, Mar 18 2017

Crossrefs

Cf. A010554, A007694, A000010, A019278.

Sequence in context: A068005 A055721 A064376 * A068578 A203812 A047894

Adjacent sequences: A283805 A283806 A283807 * A283809 A283810 A283811

Keyword

nonn

Author

Giovanni Resta, Mar 17 2017

Status

approved