A271774 a(1) = 1, then a(n) is the maximum of all 0 < m < n for which a(m) divides n.

1, 1, 2, 3, 2, 5, 2, 7, 4, 7, 2, 11, 2, 13, 6, 13, 2, 17, 2, 19, 10, 19, 2, 23, 6, 23, 4, 27, 2, 29, 2, 31, 12, 31, 10, 33, 2, 37, 16, 37, 2, 41, 2, 43, 6, 43, 2, 47, 10, 49, 18, 47, 2, 53, 12, 53, 22, 53, 2, 59, 2, 61, 10, 61, 16, 61, 2, 67, 26, 67, 2, 71, 2

Offset

1,3

Comments

If n is an odd prime, then a(n) = 2 and a(n+1) = n. All n for which a(n) = 2 are odd primes. - Robert Israel, Apr 14 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 by definition.
a(2) = 1 because a(1) divides 2.
a(3) = 2 because a(2) divides 3.
a(4) = 3 because a(3) divides 4.
a(5) = 2 because a(2) divides 5.
a(6) = 5 because a(5) divides 6.
a(7) = 2 because a(2) divides 7.
a(8) = 7 because a(7) divides 8.

Maple

A:= proc(n) option remember; local m;
    for m from n-1 by -1 do
      if n mod A(m) = 0 then return m fi
    od
end proc:
A(1):= 1:
seq(A(i), i=1..100); # Robert Israel, Apr 14 2016

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{m = n - 1}, While[Mod[n, a[m]] > 0, m--]; m]; Array[a, 100] (* Giovanni Resta, Apr 14 2016 *)

Crossrefs

Cf. A088167, A269347, A271503, A271504, A271773.

Sequence in context: A347043 A280687 A346703 * A331602 A118176 A005731

Adjacent sequences: A271771 A271772 A271773 * A271775 A271776 A271777

Keyword

nonn

Author

Peter Kagey, Apr 14 2016

Status

approved