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Search: id:A058277
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| A058277 |
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Number of values of k such that phi(k) = n, where n runs through the values (A002202) taken by phi. |
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+0
12
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| 2, 3, 4, 4, 5, 2, 6, 6, 4, 5, 2, 10, 2, 2, 7, 8, 9, 4, 3, 2, 11, 2, 2, 3, 2, 9, 8, 2, 2, 17, 2, 10, 2, 6, 6, 3, 17, 4, 2, 3, 2, 9, 2, 6, 3, 17, 2, 9, 2, 7, 2, 2, 3, 21, 2, 2, 7, 12, 4, 3, 2, 12, 2, 8, 2, 10, 4, 2, 21, 2, 2, 8, 3, 4, 2, 3, 19, 5, 2, 8, 2, 2, 6, 2, 31, 2, 9, 10
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Carmichael (1922) conjectured that the number 1 never appears in this sequence. Sierpinski conjectured and Ford (1998) proved that all integers greater than 1 occur in the sequence. Erdos (1958) proved that if s >= 1 appears in the sequence then it appears infinitely often. - Nick Hobson Nov 04 2006
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REFERENCES
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R. D. Carmichael, Note on Euler's totient function, Bull. Amer. Math. Soc. 28 (1922), pp. 109-110.
P. Erdos, Some remarks on Euler's totient function, Acta Arith. 4 (1958), pp. 10-19.
K. Ford, The Distribution of Totients, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), pp. 27-34.
E. Lucas, Theorie des Nombres, Blanchard 1958.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Totient Valence Function
N. Hobson, Problem 152, "Totient valence"
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CROSSREFS
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The nonzero terms of A014197. Cf. A000010, A002202.
Sequence in context: A108355 A057951 A076410 this_sequence A065852 A088807 A036371
Adjacent sequences: A058274 A058275 A058276 this_sequence A058278 A058279 A058280
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KEYWORD
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nonn,easy
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001
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EXTENSIONS
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More terms from Nick Hobson Nov 04 2006
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