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%I #108 Sep 04 2023 02:50:21
%S 1,1,2,1,2,2,3,1,4,2,3,2,3,3,4,1,2,4,3,2,6,3,4,2,4,3,4,3,4,4,5,1,6,2,
%T 6,4,3,3,6,2,3,6,4,3,8,4,5,2,9,4,4,3,4,4,6,3,6,4,5,4,5,5,6,1,6,6,3,2,
%U 8,6,4,4,3,3,8,3,9,6,5,2,8,3,4,6,4,4,8,3,4,8,9,4,10,5,6,2,3,9,6
%N a(n) is the maximum of A000120(k)*A000120(n/k) for divisors k of n.
%C First differs from A072084 at n = 27.
%H Robert Israel, <a href="/A349494/b349494.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = a(2*n).
%e a(45) = 8 because 45 = 3 * 15 with A072084(3) * A072084(15) = 2 * 4 = 8, and the other factorizations 1 * 45 and 5 * 9 have A072084(k) * A072084(45/k) = 4.
%p g:= proc(n) convert(convert(n,base,2),`+`) end proc:
%p f:= proc(n) local t,r;
%p max(seq(g(t)*g(n/t), t = numtheory:-divisors(n)))
%p end proc:
%p map(f, [$1..100]);
%t a[n_] := Max[(d = DigitCount[Divisors[n], 2, 1]) * Reverse[d]]; Array[a, 100] (* _Amiram Eldar_, Sep 03 2023 *)
%Y Cf. A000120, A072084.
%K nonn,base
%O 1,3
%A _Robert Israel_, Sep 03 2023
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