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Search: id:A094757
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| A094757 |
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Least k <= n such that n*pi(k) = k*pi(n), where pi(n) is the number of primes <= n (A000720). |
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4
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| 1, 2, 3, 2, 5, 2, 7, 2, 9, 10, 11, 12, 13, 14, 10, 16, 17, 18, 19, 10, 21, 22, 23, 16, 25, 26, 27, 28, 29, 27, 31, 32, 27, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 40, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: For every n there exists a k different from n (possibly k > n) such that n*pi(k) = k*pi(n). (Amarnath Murthy)
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EXAMPLE
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a(15) = 10 as 15*pi(10) = 15*4 = 60 = 10*pi(15) = 10*6.
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PROGRAM
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(PARI) {m=72; pi=vector(m, n, omega(n!)); for(n=1, m, k=1; while(n*pi[k]!=k*pi[n], k++); print1(k, ", "))}
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CROSSREFS
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Cf. A095299 for n such that a(n) < n.
Cf. A000720, A094758, A094759.
Sequence in context: A007388 A057815 A007387 this_sequence A095171 A096776 A118176
Adjacent sequences: A094754 A094755 A094756 this_sequence A094758 A094759 A094760
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 30 2004
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 01 2004
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