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Search: id:A114573
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| A114573 |
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Number n such that phi(n) is a perfect 11th power. |
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1
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| 1, 2, 3855, 4096, 4112, 4352, 5120, 5140, 5440, 6144, 6168, 6528, 7680, 7710, 8160, 5570645, 8388608, 8388736, 8421376, 8912896, 8913032, 8947712, 10485760, 10485920, 10526720, 11141120, 11141290, 11184640, 12582912, 12583104
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OFFSET
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1,2
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COMMENT
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Given the fact that phi(n) > sqrt(n) for all n except n=2 and n=6 we can see that every 11th power does appear as value only a finite number of times. What bounds on the density of this sequence can be proved?
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EXAMPLE
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phi(4096) = 2048 = 2^11
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MATHEMATICA
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For[n = 1, n < 100000, n++, If[EulerPhi[n]^(1/11) == Floor[EulerPhi[n]^(1/11)], Print[n]]]
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CROSSREFS
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Cf. A039770[square], A039771[cube], A078164[4th], A078165[5th], A078166[6th], A078167[7th], A078168[8th], A078169[9th], A078170[10th power].
Sequence in context: A065671 A117921 A094211 this_sequence A024035 A048831 A135959
Adjacent sequences: A114570 A114571 A114572 this_sequence A114574 A114575 A114576
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KEYWORD
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nonn
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AUTHOR
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Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 17 2006
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 16 2007
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