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A257977 Largest k such that there are at least k numbers b_i, 1 <= b_i <= n, each having gcd(b_i,n) >= k. 1
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 4, 1, 4, 3, 2, 1, 6, 5, 2, 3, 4, 1, 6, 1, 4, 3, 2, 5, 6, 1, 2, 3, 8, 1, 6, 1, 4, 7, 2, 1, 8, 7, 6, 3, 4, 1, 6, 5, 8, 3, 2, 1, 10, 1, 2, 9, 8, 5, 6, 1, 4, 3, 10, 1, 9, 1, 2, 7, 4, 7, 6, 1, 10, 9, 2, 1, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Initially similar to A070966, it diverges at n = 30. Here a(30) = 6, while A070966(30) = 8.

From Robert Israel, May 28 2015: (Start)

a(p^m) = p^floor(m/2) if p is prime.

a(p*q) = p if p < q are primes.

a(n) >= A033676(n). (End)

Is this the same as A034880? - R. J. Mathar, Jun 12 2015

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

EXAMPLE

Each of the four numbers 4, 6, 8, and 12 has common divisor with 12 which is no less than four. But there are no five such numbers among [1..12]. Hence a(12)=4.

MAPLE

f:= n -> nops(select(`>=`, sort(map(igcd, [$1..n], n), `>`)-[$1..n], 0)):

map(f, [$1..100]); # Robert Israel, May 28 2015

MATHEMATICA

f[n_] := Count[Reverse[Sort[GCD[Range[n], n]]] - Range[n], x_ /; x >= 0]; Table[f[n], {n, 84}]

CROSSREFS

Cf. A033676, A070966.

Sequence in context: A095165 A046805 A034880 * A070966 A219254 A072504

Adjacent sequences:  A257974 A257975 A257976 * A257978 A257979 A257980

KEYWORD

nonn

AUTHOR

Ivan Neretin, May 15 2015

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)