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Search: id:A005239
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| A005239 |
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Irregular triangle of Section I numbers. Row n contains numbers k with 2^n < k < 2^(n+1) and phi^n(k) = 2, where phi^n means n iterations of Euler's totient function.
(Formerly M2409)
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+0
2
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| 3, 5, 7, 11, 13, 15, 17, 23, 25, 29, 31, 41, 47, 51, 53, 55, 59, 61, 83, 85, 89, 97, 101, 103, 107, 113, 115, 119, 121, 123, 125, 137, 167, 179, 187, 193, 205, 221, 227, 233, 235, 239, 241, 249, 251, 253, 255, 257, 289, 353, 359, 389, 391, 401, 409
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sequence A092878 gives the number of terms in row n. Shapiro describes how the numbers x with phi^n(x)=2 can be divided into 3 sections: I: 2^n < x < 2^(n+1), II: 2^(n+1) <= x <= 3^n and III: 3^n < x <= 2*3^n. See A058812 for the numbers x for each n. - T. D. Noe (noe(AT)sspectra.com), Dec 05 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Unsolved Problems in Number Theory, B41.
Harold Shapiro, An arithmetic function arising from the phi function, Amer. Math. Monthly, Vol. 50, No. 1 (1943), 18-30.
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LINKS
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T. D. Noe, Rows n=1..22 of triangle, flattened
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EXAMPLE
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3; 5, 7; 11, 13, 15; 17, 23, 25, 29, 31; 41, 47, 51, 53, 55, 59, 61; 83,...
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MATHEMATICA
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nMax=10; nn=2^nMax; c=Table[0, {nn}]; Do[c[[n]]=1+c[[EulerPhi[n]]], {n, 2, nn}]; t={}; Do[t=Join[t, Select[Flatten[Position[c, n]], #<2^n&]], {n, nMax}]; t - T. D. Noe (noe(AT)sspectra.com), Dec 05 2007
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CROSSREFS
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Cf. A000010.
Cf. A135832 (Section I primes).
Sequence in context: A155113 A103796 A062086 this_sequence A141107 A047484 A036991
Adjacent sequences: A005236 A005237 A005238 this_sequence A005240 A005241 A005242
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net) Feb 15 1997
Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Dec 05 2007
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