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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) First differs from A034880 at a(24). - Sean A. Irvine, Sep 10 2020 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 A338669 A219254 Adjacent sequences:  A257974 A257975 A257976 * A257978 A257979 A257980 KEYWORD nonn AUTHOR Ivan Neretin, May 15 2015 STATUS approved

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Last modified May 11 16:09 EDT 2021. Contains 343794 sequences. (Running on oeis4.)