A227872 Number of odious divisors (A000069) of n.

1, 2, 1, 3, 1, 2, 2, 4, 1, 2, 2, 3, 2, 4, 1, 5, 1, 2, 2, 3, 3, 4, 1, 4, 2, 4, 1, 6, 1, 2, 2, 6, 2, 2, 3, 3, 2, 4, 2, 4, 2, 6, 1, 6, 1, 2, 2, 5, 3, 4, 1, 6, 1, 2, 3, 8, 2, 2, 2, 3, 2, 4, 3, 7, 2, 4, 2, 3, 2, 6, 1, 4, 2, 4, 2, 6, 3, 4, 2, 5, 2, 4, 1, 9, 1, 2, 2

Offset

1,2

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Formula

a(n) + A356018(n) = A000005(n).

a(2^n) = n+1. - Bernard Schott, Jul 22 2022

a(n) = 1 iff n is in A093688. - Bernard Schott, Jul 23 2022

Maple

A227872 := proc(n)
    option remember ;
    local a, d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if not isA001969(d) then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(A227872(n), n=1..200) ; # R. J. Mathar, Aug 07 2022

Mathematica

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

Prog

(PARI) a(n) = sumdiv(n, d, hammingweight(d) % 2); \\ Michel Marcus, Feb 06 2016
(PARI) isod(n) = hammingweight(n) % 2; \\ A000069
a(n) = my(v=valuation(n, 2)); n >>= v; sumdiv(n, d, isod(d)) * (v+1) \\ David A. Corneth, Jul 23 2022
(Python)
from sympy import divisors
def c(n): return bin(n).count("1")&1
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

Crossrefs

Cf. A000005, A000069, A001969, A093688, A093696, A129771, A330289, A355968, A355969, A227873 (sum odious divs.).

Sequence in context: A036989 A360330 A035197 * A323165 A091948 A339443

Adjacent sequences: A227869 A227870 A227871 * A227873 A227874 A227875

Keyword

nonn,base

Author

Vladimir Shevelev, Oct 25 2013

Extensions

More terms from Peter J. C. Moses, Oct 25 2013

Status

approved