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 A005239 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) 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, Dec 05 2007 REFERENCES 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. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Rows n=1..22 of triangle, flattened EXAMPLE 3; 5, 7; 11, 13, 15; 17, 23, 25, 29, 31; 41, 47, 51, 53, 55, 59, 61; 83,... MATHEMATICA 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, Dec 05 2007 CROSSREFS Cf. A000010. Cf. A135832 (Section I primes). Sequence in context: A103796 A179458 A062086 * A141107 A047484 A036991 Adjacent sequences:  A005236 A005237 A005238 * A005240 A005241 A005242 KEYWORD nonn,tabf AUTHOR EXTENSIONS More terms from Jud McCranie Feb 15 1997 Corrected and extended by T. D. Noe, Dec 05 2007 STATUS approved

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