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A258079
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Numbers x such that (-1)sigma(x) | sigma(x) - x, where (-1)sigma(x) is defined in A049060 and sigma(x) - x is the sum of the aliquot parts of x (A001065).
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1
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1, 2, 6, 10, 36, 168, 1098, 1204, 2840, 19488, 1881124, 3105700, 445577184, 105314212224, 134633963520, 2167649138304
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OFFSET
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1,2
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COMMENTS
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Ratio is equal to 1 for 2, 36, 1204, 2840, 1881124, 3105700, ...
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LINKS
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EXAMPLE
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(-1)sigma(1) = 1, sigma(1) - 1 = 1 - 1 = 0 and 0 / 1 = 0;
(-1)sigma(2) = 1, sigma(2) - 2 = 3 - 2 = 1 and 1 / 1 = 1;
(-1)sigma(36) = 55, sigma(36) - 36 = 91 - 36 = 55 and 55 / 55 = 1; etc.
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MAPLE
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with(numtheory): P:=proc(q) local a, b, i, j, n; for n from 1 to q do a:=ifactors(n)[2]:
b:=1; for i from 1 to nops(a) do b:=b*(-1+sum(a[i][1]^j, j=1..a[i][2])): od:
if type((sigma(n)-n)/b, integer) then print(n); fi; od; end: P(10^6);
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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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