A083210 Numbers with no subset of their divisors such that the complement has the same sum.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91

Offset

1,2

Comments

A083206(a(n)) = 0; complement of A083207; deficient numbers (A005100) are a subset.

A179529(a(n)) = 0. [Reinhard Zumkeller, Jul 19 2010]

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Reinhard Zumkeller, Illustration of initial terms

Prog

(Python)
from itertools import count, islice
from sympy import divisors
def A083210_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue, 1)):
        d = divisors(n)
        s = sum(d)
        if s&1^1 and n<<1<=s:
            d = d[:-1]
            s2, ld = (s>>1)-n, len(d)
            z = [[0 for _ in range(s2+1)] for _ in range(ld+1)]
            for i in range(1, ld+1):
                y = min(d[i-1], s2+1)
                z[i][:y] = z[i-1][:y]
                for j in range(y, s2+1):
                    z[i][j] = max(z[i-1][j], z[i-1][j-y]+y)
                if z[i][s2] == s2:
                    break
            else:
                yield n
        else:
            yield n
A083210_list = list(islice(A083210_gen(), 30)) # Chai Wah Wu, Feb 13 2023
(PARI) is_A083210(n) = !A083206(n); \\ Antti Karttunen, Dec 02 2024

Crossrefs

Positions of 0's in A083206.

Cf. A083207 (complement).

Cf. A005100, A083211 (subsequences).

Sequence in context: A286291 A286926 A145198 * A345913 A187392 A232741

Adjacent sequences: A083207 A083208 A083209 * A083211 A083212 A083213

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2003

Status

approved