A283808 - OEIS

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

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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