A078170 Numbers k such that phi(k) is a perfect tenth power.

1, 2, 1285, 2048, 2056, 2176, 2560, 2570, 2720, 3072, 3084, 3264, 3840, 4080, 1114129, 2097152, 2097184, 2105344, 2228224, 2228258, 2236928, 2621440, 2621480, 2631680, 2785280, 2796160, 3145728, 3145776, 3158016, 3342336

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..2250

Example

phi of the sequence includes 1, 1024, 1048576,.. etc.; powers emerge several times; a(3) = A053576(10) = 1285; in sequence smoother ranges and quite large jumps alternate when power of new numbers appear as phi-values.

Mathematica

k=10; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 10000000}]

Prog

(PARI) is(n)=ispower(eulerphi(n), 10) \\ Charles R Greathouse IV, Apr 24 2020

Crossrefs

Cf. A039770 (square), A039771 (cube), A078164 (4th), A078165 (5th), A078166 (6th), A078167 (7th), A078168 (8th), A078169 (9th), A078170 (10th power, this sequence), A001317, A053576, A045544, A000010.

Sequence in context: A369777 A171940 A160003 * A062663 A295187 A345402

Adjacent sequences: A078167 A078168 A078169 * A078171 A078172 A078173

Keyword

nonn

Author

Labos Elemer, Nov 27 2002

Status

approved