A349494 a(n) is the maximum of A000120(k)*A000120(n/k) for divisors k of n.

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, 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, 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

Offset: 1

Author

Robert Israel, Sep 03 2023

Keywords

• nonn
• base

Comments

First differs from A072084 at n = 27.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000120, A072084.

Programs

Maple

g:= proc(n) convert(convert(n,base,2),`+`) end proc:
f:= proc(n) local t,r;
      max(seq(g(t)*g(n/t), t = numtheory:-divisors(n)))
    end proc:
map(f, [$1..100]);

Mathematica

a[n_] := Max[(d = DigitCount[Divisors[n], 2, 1]) * Reverse[d]]; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)

Formula

a(n) = a(2*n).