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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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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 (Jan., 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).
Adjacent sequences: A005236 A005237 A005238 this_sequence A005240 A005241 A005242
Sequence in context: A056911 A103796 A062086 this_sequence A141107 A047484 A036991
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from j.mccranie(AT)comcast.net (Jud Mccranie) 2/97.
Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Dec 05 2007
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