

A283808


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 114117.


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 xrange(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



