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A049603
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(1+e)-sigma perfect numbers: (1+e) - sigma(x) = 2*x.
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6
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6, 28, 264, 1104, 3360, 75840, 6499584, 151062912, 2171581440, 4686409728, 316023611904
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OFFSET
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1,1
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COMMENTS
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The function (1+e) - sigma(n) is defined in A051378. This sequence lists solutions to A051378(n) = 2*n.
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LINKS
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EXAMPLE
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Factorizations: 2*3, 2^2*7, 2^3*3*11, 2^4*3*23, 2^5*3*5*7, 2^6*3*5*79, 2^8*3^2*7*13*31, 2^7*3^2*7*11*13*131, 2^10*3*5*7*19*1063.
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MATHEMATICA
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(* Assuming all terms greater than 28 are multiple of 24 *) ok[n_] := 2*n == Times @@ (1 + Sum[First[#]^s, {s, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; Reap[For[n = 2, n <= 2171581440, n = n + If[n < 48, 1, 24], If[ok[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jun 26 2012 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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