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A057237 Maximum k <= n such that 1, 2, ..., k are all relatively prime to n. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

For n >= 2, a(n) = (smallest prime dividing n) - 1 = A020639(n) - 1.

For n >= 2, a(n) = (n-1) mod (smallest prime dividing n); cf. A083218. - Reinhard Zumkeller, Apr 22 2003

EXAMPLE

a(25) = 4 because 1, 2, 3 and 4 are relatively prime to 25.

MATHEMATICA

Join[{1}, Table[Length[Split[Boole[CoprimeQ[n, Range[n-1]]]][[1]]], {n, 2, 100}]] (* Harvey P. Dale, Dec 28 2021 *)

PROG

(PARI) a(n) = if (n==1, 1, factor(n)[1, 1] - 1); \\ Michel Marcus, May 29 2015

CROSSREFS

Cf. A020639, A083218.

Cf. A066169.

Sequence in context: A346466 A258409 A060680 * A187730 A049559 A063994

Adjacent sequences: A057234 A057235 A057236 * A057238 A057239 A057240

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 20 2000

STATUS

approved

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Last modified November 26 20:01 EST 2022. Contains 358362 sequences. (Running on oeis4.)