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A281016 Numbers n such that n, phi(n) and cototient(n) are all perfect powers. 1
8, 16, 32, 64, 125, 128, 256, 512, 1024, 2048, 3125, 4096, 4913, 8192, 16384, 32768, 50653, 65536, 78125, 131072, 262144, 524288, 1030301, 1048576, 1419857, 1953125, 2097152, 4194304, 7645373, 8388608, 16777216, 16974593, 33554432, 35831808, 48828125, 64481201, 67108864, 69343957 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence does not contain only prime powers. Least term that has a prime factor which is not of the form m^2 + 1 is 35831808 = 2^14 * 3^7. The next one is 102503232 = 2^6 * 3^6 * 13^3. There are infinitely many such numbers.

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

125 = 5^3 is a term because phi(5^3) = 10^2 and cototient(5^3) = 5^2.

MATHEMATICA

Select[Range[10^6], Times @@ Boole@ Map[Or[# == 1, GCD @@ FactorInteger[#][[All, 2]] > 1] &, {#, EulerPhi@ #, # - EulerPhi@ #}] > 0 &] (* Michael De Vlieger, Jan 14 2017 *)

PROG

(PARI) is(n) = ispower(eulerphi(n)) && ispower(n-eulerphi(n)) && ispower(n);

CROSSREFS

Cf. A000010, A001597, A051953, A054754, A166955.

Sequence in context: A192135 A345053 A256817 * A048169 A089882 A335850

Adjacent sequences:  A281013 A281014 A281015 * A281017 A281018 A281019

KEYWORD

nonn

AUTHOR

Altug Alkan, Jan 13 2017

STATUS

approved

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Last modified December 9 03:18 EST 2021. Contains 349625 sequences. (Running on oeis4.)