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A135832
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Irregular triangle of Section I primes. Row n contains primes p with 2^n < p < 2^(n+1) and phi^n(p) = 2, where phi^n means n iterations of Euler's totient function.
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6
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3, 5, 7, 11, 13, 17, 23, 29, 31, 41, 47, 53, 59, 61, 83, 89, 97, 101, 103, 107, 113, 137, 167, 179, 193, 227, 233, 239, 241, 251, 257, 353, 359, 389, 401, 409, 443, 449, 461, 467, 479, 499, 503, 641, 719, 769, 773, 809, 821, 823, 857, 881, 887, 929, 941, 953
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OFFSET
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1,1
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COMMENTS
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Sequence A135833 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. The primes in section I are fairly sparce. All other primes belong to section II. Section III consists of only even numbers. See A058812 for the numbers x for each n.
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REFERENCES
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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; 17, 23, 29, 31; 41, 47, 53, 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 && PrimeQ[ # ]&]], {n, nMax}]; t
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CROSSREFS
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Cf. A135834 (Section II primes).
Sequence in context: A090670 A074832 A075794 * A074781 A147545 A083668
Adjacent sequences: A135829 A135830 A135831 * A135833 A135834 A135835
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KEYWORD
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nonn,tabf
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AUTHOR
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T. D. Noe, Nov 30 2007
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STATUS
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approved
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