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A317582 a(n) is the number of k with 1 <= k <= n-1 such that a(k) * a(n-k) <= n. 3

%I

%S 0,1,2,3,4,5,6,6,4,4,4,6,8,8,8,8,6,7,8,9,10,9,6,6,6,8,10,14,12,12,10,

%T 8,10,12,14,14,14,8,6,10,12,18,16,14,12,9,12,15,20,21,18,16,8,12,18,

%U 20,16,16,14,14,14,14,20,23,18,16,16,14,18,22,22,22,16

%N a(n) is the number of k with 1 <= k <= n-1 such that a(k) * a(n-k) <= n.

%C This sequence can be described as a(n) = Sum_{k=1..n-1} [Q(a(k), a(n-k), n] for some predicate Q in three variables, one of which corresponds to n; in that sense, this is a generalization of the sequences described in A317420.

%C See A317596 and A317638 for similar sequences.

%H Rémy Sigrist, <a href="/A317582/b317582.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 9:

%e - a(1) * a(8) = 0 * 6 = 0 <= 9,

%e - a(2) * a(7) = 1 * 6 = 6 <= 9,

%e - a(3) * a(6) = 2 * 5 = 10 > 9,

%e - a(4) * a(5) = 3 * 4 = 12 > 9,

%e - a(5) * a(4) = 4 * 3 = 12 > 9,

%e - a(6) * a(3) = 5 * 2 = 10 > 9,

%e - a(7) * a(2) = 6 * 1 = 6 <= 9,

%e - a(8) * a(1) = 6 * 0 = 0 <= 9,

%e - hence a(9) = 4.

%o (PARI) a = vector(73); for (n=1, #a, a[n] = sum(k=1, n-1, a[k]*a[n-k] <= n); print1 (a[n] ", "))

%Y Cf. A317420, A317596, A317638.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Aug 01 2018

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)