A212302 -id:A212302 - cp's OEIS frontend

A227873 Sum of odious divisors of n. See A000069 for odious numbers.

1, 3, 1, 7, 1, 3, 8, 15, 1, 3, 12, 7, 14, 24, 1, 31, 1, 3, 20, 7, 29, 36, 1, 15, 26, 42, 1, 56, 1, 3, 32, 63, 12, 3, 43, 7, 38, 60, 14, 15, 42, 87, 1, 84, 1, 3, 48, 31, 57, 78, 1, 98, 1, 3, 67, 120, 20, 3, 60, 7, 62, 96, 29, 127, 14, 36, 68, 7, 70, 129, 1, 15

Offset: 1

Vladimir Shevelev, Oct 25 2013

Sum of evil divisors of n is A000203(n) - a(n) = A260934(n). See A001969 for evil numbers.

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

Cf. A000203, A227872, A000069, A001969, A212302, A260934, A010060, A102392.

A227873 := proc(n)
    option remember ;
    local a,d ;
    a := 0 ;
    for d in numtheory[divisors](n) do
        if not isA001969(d) then
            a := a+d ;
        end if;
    end do:
    a ;
end proc:
seq(A227873(n),n=1..200) ; # R. J. Mathar, Aug 17 2022

Total[Select[Divisors@ #, OddQ@ First@ DigitCount[#, 2] &]] & /@ Range@ 72 (* Michael De Vlieger, Aug 04 2015 *)

a(n) = sumdiv(n, d, d*(hammingweight(d) % 2)); \\ Michel Marcus, Aug 04 2015

a(n) = Sum_{d|n} A102392(d). - Ridouane Oudra, Apr 19 2025

More terms from Peter J. C. Moses

Minor changes. - Wolfdieter Lang, Aug 23 2015

A230587 Number n such that the sum of its proper evil divisors (A001969) equals n.

Original entry on oeis.org

18, 476, 1484, 1988, 2324, 3164, 4172, 4564, 5516, 7196, 7364, 7532, 8036, 8876, 9716, 9772, 10052, 10444, 10892, 11956, 12572, 13076, 13412, 14084, 16604, 16772, 18004, 19866, 20692, 21328, 21364, 21644, 22316, 22988, 23492, 23884, 23996, 24164, 24668, 24836

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, Oct 24 2013

Sequence could be called the "evil-perfect numbers".
By the Euclid-Euler theorem, an even number n is perfect (A000396) if and only if n=2^(k-1)*(2^k-1), where 2^k-1 is prime. From this it follows that all even perfect numbers more than 6 have only odious divisors (A000069). In contrast to them, this sequence lists those abundant numbers n (A005101), all proper evil divisors of which sum to n.
It is asked, are there non-perfect numbers n, all proper odious divisors of which sum to n? The first two such numbers were found by Giovanni Resta, see A212302.

			18 is in the sequence since its proper divisors are {1, 2, 3, 6, 9}, and their subset that is in A001969 is {3, 6, 9} whose sum is 18.

Amiram Eldar, Table of n, a(n) for n = 1..10000
V. Shevelev, A question concerning perfect numbers

Cf. A000396, A005101, A001969, A000069.

aQ[n_] := DivisorSum[n, # &, # < n && EvenQ[DigitCount[#, 2][[1]]] &] == n; Select[Range[25000], aQ] (* Amiram Eldar, Jun 21 2019 *)

is(n)=sumdiv(n,d,if(hammingweight(d)%2==0 && dCharles R Greathouse IV, Oct 24 2013

cp's OEIS Frontend

A227873 Sum of odious divisors of n. See A000069 for odious numbers.

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