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A175591
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a(n) = (sigma(n-th Zumkeller number)/2) - (n-th Zumkeller number).
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1
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0, 2, 1, 6, 0, 6, 5, 6, 14, 6, 4, 24, 6, 2, 6, 13, 28, 2, 27, 30, 6, 1, 32, 12, 6, 60, 30, 36, 6, 28, 36, 40, 29, 72, 6, 10, 93, 6, 62, 36, 48, 9, 78, 84, 32, 6, 28, 52, 39, 132, 6, 112, 6, 34, 96, 90, 7, 60, 80, 6, 48, 134, 6, 45, 28, 108, 6, 61, 102, 160, 38, 48, 72, 22, 26, 6, 225, 28, 6
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OFFSET
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1,2
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LINKS
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FORMULA
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PROG
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(Python)
from sympy import divisors
import numpy as np
for n in range(1, 10**6):
....d = divisors(n)
....s = sum(d)
....if not s % 2 and 2*n <= s:
........d.remove(n)
........s2, ld = int(s/2-n), len(d)
........z = np.zeros((ld+1, s2+1), dtype=int)
........for i in range(1, ld+1):
............y = min(d[i-1], s2+1)
............z[i, range(y)] = z[i-1, range(y)]
............z[i, range(y, s2+1)] = np.maximum(z[i-1, range(y, s2+1)], z[i-1, range(0, s2+1-y)]+y)
............if z[i, s2] == s2:
................break
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Inserted a(45) and corrected a(73) by Chai Wah Wu, Aug 20 2014
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STATUS
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approved
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