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A365476 a(n) is the minimum of A000120(k)*A000120(A071904(n)/k) for divisors k of the n-th odd composite number A071904(n) other than 1 and A071904(n).

%I A365476 #21 Aug 02 2024 12:05:00
%S A365476 4,4,6,4,4,6,6,6,4,9,4,6,6,6,6,8,6,9,4,4,8,9,10,6,4,6,6,8,6,6,9,6,6,8,
%T A365476 9,8,10,9,8,6,4,10,8,12,4,9,6,6,10,10,6,6,6,4,6,12,6,6,9,8,8,15,6,6,6,
%U A365476 6,10,10,6,6,9,8,12,8,9,8,8,8,9,9,10,8,9,4,6,10,4,12,12,8,10,10,6
%N A365476 a(n) is the minimum of A000120(k)*A000120(A071904(n)/k) for divisors k of the n-th odd composite number A071904(n) other than 1 and A071904(n).
%C A365476 a(n) = 4 iff A071904(n) is the product of two (not necessarily distinct) members of A000051.
%C A365476 a(n) >= A000120(A071904(n)) because A000120(x) * A000120(y) >= A000120(x*y).
%C A365476 a(n) <= A349494(A071904(n)).
%H A365476 Robert Israel, <a href="/A365476/b365476.txt">Table of n, a(n) for n = 1..10000</a>
%e A365476 a(9) = 4 because A071904(9) = 45 = 3 * 15 = 5 * 9 with A000120(3) * A000120(15) = 2 * 4 = 8 and A000120(5) * A000120(9) = 2 * 2 = 4.
%p A365476 g:= proc(n) convert(convert(n, base, 2), `+`) end proc:
%p A365476 f:= proc(n) local t, r;
%p A365476       min(seq(g(t)*g(n/t), t = numtheory:-divisors(n) minus {1,n}))
%p A365476     end proc:
%p A365476 map(f, remove(isprime, [seq(i,i=3..1000,2)]));
%o A365476 (Python)
%o A365476 from sympy import primepi, divisors
%o A365476 def A365476(n):
%o A365476     if n == 1: return 4
%o A365476     m, k = n, primepi(n) + n + (n>>1)
%o A365476     while m != k:
%o A365476         m, k = k, primepi(k) + n + (k>>1)
%o A365476     return min(int(d).bit_count()*int(m//d).bit_count() for d in divisors(m,generator=True) if 1<d<m) # _Chai Wah Wu_, Aug 02 2024
%Y A365476 Cf. A000051, A000120, A071904, A349494.
%K A365476 nonn,base
%O A365476 1,1
%A A365476 _Robert Israel_, Sep 04 2023