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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).
1
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, 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, 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
OFFSET
1,1
COMMENTS
a(n) = 4 iff A071904(n) is the product of two (not necessarily distinct) members of A000051.
a(n) >= A000120(A071904(n)) because A000120(x) * A000120(y) >= A000120(x*y).
a(n) <= A349494(A071904(n)).
LINKS
EXAMPLE
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.
MAPLE
g:= proc(n) convert(convert(n, base, 2), `+`) end proc:
f:= proc(n) local t, r;
min(seq(g(t)*g(n/t), t = numtheory:-divisors(n) minus {1, n}))
end proc:
map(f, remove(isprime, [seq(i, i=3..1000, 2)]));
PROG
(Python)
from sympy import primepi, divisors
def A365476(n):
if n == 1: return 4
m, k = n, primepi(n) + n + (n>>1)
while m != k:
m, k = k, primepi(k) + n + (k>>1)
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Sep 04 2023
STATUS
approved