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Search: id:A080289
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| A080289 |
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Integers n for which the ratio phi(n)/pi(n) is smaller than for any subsequent n. Here phi(n) is Euler's totient function and pi(n) is the number of primes that are at most n. |
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| 6, 12, 30, 42, 60, 90, 210, 420, 630, 840, 1050, 2310, 2730, 3570, 4620, 5460, 6930, 9240, 11550, 13860, 30030, 39270, 43890, 60060, 90090
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Discovered whilst proving that phi(n)>2pi(n) for all n, to prove a conjecture on www.primepuzzles.net. The conjecture stated that for all sufficiently large even n, n is the sum of two coprime composite numbers. This is in fact true for all even n>210. For more details email the author.
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LINKS
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C. Rivera, Perry's conjecture
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EXAMPLE
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For all n>90090, phi(n)/pi(n)>2>17280/8726=1.9803.
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CROSSREFS
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Sequence in context: A079390 A124679 A083494 this_sequence A126857 A071342 A125056
Adjacent sequences: A080286 A080287 A080288 this_sequence A080290 A080291 A080292
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KEYWORD
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nonn
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AUTHOR
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Luke Pebody (ltp1000(AT)hermes.cam.ac.uk), Feb 13 2003
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