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A223137
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Numbers n such that sigma(n+1) - sigma(n-1) = k*n for some integer k, where sigma(n) = A000203 (sum of divisors of n).
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2
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5, 34, 55, 285, 367, 835, 849, 919, 1241, 1505, 2911, 2914, 3305, 4149, 4188, 6111, 6903, 7170, 7913, 9360, 10251, 10541, 12566, 15086, 17273, 17815, 19005, 19689, 21411, 21462, 24882, 25020, 26610, 28125, 30593, 30789, 31485, 38211, 38983, 39787, 40311, 45355
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OFFSET
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1,1
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COMMENTS
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Supersequence of A055574 for k=0 (n satisfying sigma(n+1) = sigma(n-1)). For number 5 is k=1. Are there other such number for k=1 or k=-1?
Corresponding values of integers k: 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,....
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LINKS
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EXAMPLE
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Number 5 is in sequence because sigma(6) - sigma(4) = 12 - 7 = 5 = 1 * 5; k=1.
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MATHEMATICA
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Select[Range[100000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1])/#] &] (* T. D. Noe, May 02 2013 *)
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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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STATUS
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approved
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