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).

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

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

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

Cf. A000051, A000120, A071904, A349494.

Sequence in context: A059656 A205373 A064041 * A241656 A275161 A077553

Adjacent sequences: A365473 A365474 A365475 * A365477 A365478 A365479

Keyword

nonn,base

Author

Robert Israel, Sep 04 2023

Status

approved