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A349494
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a(n) is the maximum of A000120(k)*A000120(n/k) for divisors k of n.
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3
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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
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OFFSET
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1,3
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COMMENTS
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First differs from A072084 at n = 27.
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LINKS
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FORMULA
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a(n) = a(2*n).
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EXAMPLE
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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.
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MAPLE
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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]);
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MATHEMATICA
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a[n_] := Max[(d = DigitCount[Divisors[n], 2, 1]) * Reverse[d]]; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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