A397099 Excluding powers of 2 and perfect numbers, numbers whose abundancy is closer to 2 than any smaller number.

3, 9, 10, 18, 20, 44, 70, 88, 104, 136, 464, 650, 1888, 1952, 4030, 5830, 8384, 17816, 18632, 32128, 32896, 116624, 130304, 442365, 521728, 522752, 1848964, 5546958, 5546994, 5547018, 5547138, 5547162, 5547174, 5547306, 5547342, 5547606, 5547702, 5547846

Offset

1,1

Comments

The smallest n values where a(n) is odd are 1, 2, 24, and 95166.

For n > 22, the smallest n values where a(n) is deficient are 95163, 95165, and 95166.

Links

Hoang Nguyen, Table of n, a(n) for n = 1..10000

Example

3's abundancy is (1+3)/3 = 4/3, which is 2/3 away from 2.
9's abundancy is (1+3+9)/9 = 13/9, which is 5/9 (< 2/3) away from 2.
10's abundancy is (1+2+5+10)/10 = 9/5, which is 1/5 (< 5/9) away from 2.

Prog

(Julia)
using Primes
function a(n)
    min = 2
    i = 1
    num = 0
    while i <= n
        num += 1
        diff = abs(sum(divisors(num)) // num - 2)
        if diff < min && diff != 0 && !ispow2(num)
            min = diff
            print("$num, ")
            i += 1
        end
    end
end

Crossrefs

Subsequence of the union of A071927 and A228450.

Cf. A171929.

Sequence in context: A030794 A134073 A088005 * A340459 A125237 A085459

Adjacent sequences: A397094 A397096 A397097 * A397100 A397102 A397103

Keyword

nonn,new

Author

Hoang Nguyen, Jun 16 2026

Status

approved