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, 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

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: A355366 A046805 A034880 * A070966 A338669 A219254

Adjacent sequences: A257974 A257975 A257976 * A257978 A257979 A257980

Keyword

nonn

Author

Ivan Neretin, May 15 2015

Status

approved