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Search: id:A007374
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| A007374 |
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Smallest k such that phi(x) = k has exactly n solutions.
(Formerly M1093)
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+0
11
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| 1, 2, 4, 8, 12, 32, 36, 40, 24, 48, 160, 396, 2268, 704, 312, 72, 336, 216, 936, 144, 624, 1056, 1760, 360, 2560, 384, 288, 1320, 3696, 240, 768, 9000, 432, 7128, 4200, 480, 576, 1296, 1200, 15936, 3312, 3072, 3240, 864, 3120, 7344, 3888, 720, 1680, 4992
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Carmichael conjectured that no term exists for n=1.
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 2..778
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Phi function.
Eric Weisstein's World of Mathematics, Carmichael's Totient Function Conjecture.
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MATHEMATICA
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a = Table[ 0, {10^5} ]; Do[ s = EulerPhi[ n ]; If[ s < 100001, a[ [ s ] ]++ ], {n, 1, 10^6} ]; Do[ k = 1; While[ a[ [ k ] ] != n, k++ ]; Print[ k ], {n, 2, 75} ]
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CROSSREFS
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Cf. A000010. Essentially same as A014573. Records in A105207, A105208. See also A097942.
Cf. A105207, A105208.
Sequence in context: A082906 A085083 A076745 this_sequence A105207 A133802 A076202
Adjacent sequences: A007371 A007372 A007373 this_sequence A007375 A007376 A007377
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Link fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 06 2009
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