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A307043
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Numbers n such that A307042(n) = Sum_{k=1..n} esigma(k) is divisible by n, where esigma(k) is sum of exponential divisors of k (A051377).
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4
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1, 3, 4, 8, 13, 78, 94, 481, 511, 4819, 13557, 23083, 84245, 204744, 562243, 591105, 614339, 617675, 656263, 1545716, 6370802, 34882737, 534034248, 601990019, 1153304776, 2064184733, 3570196547, 10572032882
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OFFSET
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1,2
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COMMENTS
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The exponential version of A056550.
The corresponding quotients are 1, 2, 3, 5, 8, 45, ... (see the link for more values).
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LINKS
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EXAMPLE
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3 is in the sequence since esigma(1) + esigma(2) + esigma(3) = 1 + 2 + 3 = 6 is divisible by 3.
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MATHEMATICA
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esigma[n_] := Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; seq={}; s = 0; Do[s = s + esigma [n]; If[Divisible[s, n], AppendTo[seq, n]], {n, 1, 10^6}]; seq (* after Jean-François Alcover at A051377 *)
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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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STATUS
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approved
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