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A079277
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a(1) = 0; for n>1, a(n) is the largest integer < n such that any prime factor of a(n) is also a prime factor of n.
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1
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0, 1, 1, 2, 1, 4, 1, 4, 3, 8, 1, 9, 1, 8, 9, 8, 1, 16, 1, 16, 9, 16, 1, 18, 5, 16, 9, 16, 1, 27, 1, 16, 27, 32, 25, 32, 1, 32, 27, 32, 1, 36, 1, 32, 27, 32, 1, 36, 7, 40, 27, 32, 1, 48, 25, 49, 27, 32, 1, 54, 1, 32, 49, 32, 25, 64, 1, 64, 27, 64, 1, 64, 1, 64, 45, 64, 49, 72, 1, 64, 27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The function a(n) complements Eulers phi-function: 1) a(n)+phi(n)=n if n is a power of a prime. 2) It seems also that a(n)+phi(n)>=n for "almost all numbers". 3) a(2n)=n+1 if and only if n is a Mersenne prime. 4) Lim a(n^k)/n^k =1 if n has at least two prime factors and k goes to infinity.
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LINKS
| David W. Wilson, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(10)=8 since 8 is the largest integer< 10 that can be written using only the primes 2 and 5. a(78)=72 since 72 is the largest number less than 78 that can be written using only the primes 2, 3 and 13. (78=2*3*13).
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CROSSREFS
| Sequence in context: A063717 A024994 A051953 * A066452 A007104 A102627
Adjacent sequences: A079274 A079275 A079276 * A079278 A079279 A079280
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KEYWORD
| nonn
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AUTHOR
| Istvan Beck (istbe(AT)online.no), Feb 07 2003
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