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A083210
Numbers with no subset of their divisors such that the complement has the same sum.
5
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]
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
CROSSREFS
Cf. A083211.
Sequence in context: A286291 A286926 A145198 * A345913 A187392 A232741
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 22 2003
STATUS
approved