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A335069
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Numbers k where records occur for phi(k+1)/phi(k), where phi is the Euler totient function (A000010).
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1
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1, 2, 6, 30, 210, 2310, 30030, 120120, 690690, 1021020, 2042040, 4084080, 9699690, 58198140, 96996900, 106696590, 223092870, 892371480, 6469693230, 6915878970, 19409079690, 32348466150, 71166625530, 200560490130, 7420738134810, 8624101075590
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OFFSET
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1,2
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COMMENTS
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Somayajulu (1950) proved that phi(k+1)/phi(k) is unbounded, hence this sequence is infinite.
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REFERENCES
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József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 16.
B. S. K. R. Somayajulu, On Euler's totient function phi(n), Math. Student, Vol. 18 (1950), pp. 31-32.
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LINKS
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EXAMPLE
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The values of phi(k+1)/phi(k) for the first terms are 1, 2, 3, 3.75, 4.375, 4.8125, ...
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MATHEMATICA
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rm = 0; s1 = 1; seq = {}; Do[s2 = EulerPhi[n]; If[(r = s2/s1) > rm, rm = r; AppendTo[seq, n-1]]; s1 = s2, {n, 2, 10^6}]; seq
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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