A356018 a(n) is the number of evil divisors (A001969) of n.

0, 0, 1, 0, 1, 2, 0, 0, 2, 2, 0, 3, 0, 0, 3, 0, 1, 4, 0, 3, 1, 0, 1, 4, 1, 0, 3, 0, 1, 6, 0, 0, 2, 2, 1, 6, 0, 0, 2, 4, 0, 2, 1, 0, 5, 2, 0, 5, 0, 2, 3, 0, 1, 6, 1, 0, 2, 2, 0, 9, 0, 0, 3, 0, 2, 4, 0, 3, 2, 2, 1, 8, 0, 0, 4, 0, 1, 4, 0, 5, 3, 0, 1, 3, 3, 2

Offset

1,6

Comments

a(n) = 0 iff n is in A093696.

Links

Table of n, a(n) for n=1..86.

Formula

a(n) = A000005(n) - A227872(n).

Example

12 has 6 divisors: {1, 2, 3, 4, 6, 12} of which three {3, 6, 12} have an even number of 1's in their binary expansion with 11, 110 and 11100 respectively; hence a(12) = 3.

Maple

A356018 := proc(n)
    local a, d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if isA001969(d) then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A356018(n), n=1..200) ;  # R. J. Mathar, Aug 07 2022

Mathematica

a[n_] := DivisorSum[n, 1 &, EvenQ[DigitCount[#, 2, 1]] &]; Array[a, 100] (* Amiram Eldar, Jul 23 2022 *)

Prog

(Python)
from sympy import divisors
def c(n): return bin(n).count("1")&1 == 0
def a(n): return sum(1 for d in divisors(n, generator=True) if c(d))
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Jul 23 2022
(PARI) a(n) = my(v = valuation(n, 2)); n>>=v; d=divisors(n); sum(i=1, #d, bitand(hammingweight(d[i]), 1) == 0) * (v+1) \\ David A. Corneth, Jul 23 2022

Crossrefs

Cf. A000005, A001969, A093688, A093696 (location of 0s), A227872, A356019, A356020.

Similar sequences: A083230, A087990, A087991, A332268, A355302.

Sequence in context: A275966 A284059 A329767 * A107502 A230419 A146165

Adjacent sequences: A356015 A356016 A356017 * A356019 A356020 A356021

Keyword

nonn,easy,base

Author

Bernard Schott, Jul 23 2022

Extensions

More terms from David A. Corneth, Jul 23 2022

Status

approved