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A057237
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Maximum k <= n such that 1, 2, ..., k are all relatively prime to n.
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8
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1, 1, 2, 1, 4, 1, 6, 1, 2, 1, 10, 1, 12, 1, 2, 1, 16, 1, 18, 1, 2, 1, 22, 1, 4, 1, 2, 1, 28, 1, 30, 1, 2, 1, 4, 1, 36, 1, 2, 1, 40, 1, 42, 1, 2, 1, 46, 1, 6, 1, 2, 1, 52, 1, 4, 1, 2, 1, 58, 1, 60, 1, 2, 1, 4, 1, 66, 1, 2, 1, 70, 1, 72, 1, 2, 1, 6, 1, 78, 1, 2, 1, 82, 1, 4, 1, 2, 1, 88, 1, 6, 1, 2, 1
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OFFSET
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1,3
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COMMENTS
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In reduced residue system for n [=RRS(n)] the [initial] segment of consecutive integers, i.e. of which no number is missing is {1,2,....,a[n]}. The first missing term from RRS(n) is 1+a(n), the least prime divisor.. E.g. n=121 : RRS[121] = {1,2,3,4,5,6,7,8,9,10,lag,12,..}, i.e. no 11 is in RRS; a[n] is the length of longest lag-free number segment consisting of consecutive integers, since A020639[n] divides n. - Labos Elemer, May 14 2003
a(n) is also the difference between the smallest two divisors of n, (the column 1 of A193829), if n >= 2. - Omar E. Pol, Aug 31 2011
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LINKS
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FORMULA
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For n >= 2, a(n) = (smallest prime dividing n) - 1 = A020639(n) - 1.
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EXAMPLE
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a(25) = 4 because 1, 2, 3 and 4 are relatively prime to 25.
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MATHEMATICA
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Join[{1}, Table[Length[Split[Boole[CoprimeQ[n, Range[n-1]]]][[1]]], {n, 2, 100}]] (* Harvey P. Dale, Dec 28 2021 *)
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PROG
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(PARI) a(n) = if (n==1, 1, factor(n)[1, 1] - 1); \\ Michel Marcus, May 29 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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