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A334410
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Numbers m such that the sum of the first k divisors of m, for some k, is equal to the sum of its other divisors.
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3
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6, 28, 120, 496, 672, 8128, 35640, 199584, 523776, 2142720, 12999168, 33550336, 459818240, 1476304896, 2836487808, 6039429120, 6399679104, 8589869056, 36639203328, 51001180160, 137438691328, 266653296000, 658470384000, 2732372020224, 6164773235712
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OFFSET
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1,1
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COMMENTS
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Includes all the perfect numbers (A000396), for them k = d(m) - 1 and the even 3-perfect numbers (A005820), for them k = d(m) - 2 (where d(m) = A000005(m) is the number of divisors of m).
36639203328 is also a term.
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LINKS
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EXAMPLE
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6 is a term since its set of divisors, {1, 2, 3, 6}, can be partitioned into two disjoint sets with equal sum, {1, 2, 3} and {6}, such that the first 3 divisors are in the first set.
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MATHEMATICA
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Select[Range[200000], MemberQ[Accumulate[(d = Divisors[#])], (Plus @@ d)/2] &]
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PROG
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(Python)
from itertools import count, islice
from sympy import divisors
def A334410_gen(startvalue=1): # generator of terms >= startvalue
for n in count(max(startvalue, 1)):
ds = divisors(n)
s = sum(ds)
if s % 2 == 0 and any(2*a==s for a in accumulate(ds)):
yield n
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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