A227872 - OEIS

%I #45 Aug 17 2022 12:30:25

%S 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,

%T 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,

%U 2,6,1,4,2,4,2,6,3,4,2,5,2,4,1,9,1,2,2

%N Number of odious divisors (A000069) of n.

%H Peter J. C. Moses, <a href="/A227872/b227872.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(2^n) = n+1. - _Bernard Schott_, Jul 22 2022

%F a(n) = 1 iff n is in A093688. - _Bernard Schott_, Jul 23 2022

%p A227872 := proc(n)

%p     option remember ;

%p     local a,d ;

%p     a := 0 ;

%p     for d in numtheory[divisors](n) do

%p         if not isA001969(d) then

%p             a := a+1 ;

%p         end if;

%p     end do:

%p     a ;

%p end proc:

%p seq(A227872(n),n=1..200) ; # _R. J. Mathar_, Aug 07 2022

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

%o (PARI) a(n) = sumdiv(n, d, hammingweight(d) % 2); \\ _Michel Marcus_, Feb 06 2016

%o (PARI) isod(n) = hammingweight(n) % 2; \\ A000069

%o a(n) = my(v=valuation(n, 2)); n >>= v; sumdiv(n,d,isod(d)) * (v+1) \\ _David A. Corneth_, Jul 23 2022

%o (Python)

%o from sympy import divisors

%o def c(n): return bin(n).count("1")&1

%o def a(n): return sum(1 for d in divisors(n, generator=True) if c(d))

%o print([a(n) for n in range(1, 101)]) # _Michael S. Branicky_, Jul 23 2022

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

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Oct 25 2013

%E More terms from _Peter J. C. Moses_, Oct 25 2013