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A357493
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Numbers k such that s(k) = 3*k, where s(k) is the sum of divisors of k that have a square factor (A162296).
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5
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OFFSET
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1,1
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COMMENTS
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Analogous to 3-perfect numbers (A005820) with nonsquarefree divisors.
Equivalently, numbers k such that A325314(k) = -2*k.
a(11) > 10^11, if it exists.
If k is one of the 6 known 3-perfect numbers, then 4*k is a term.
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LINKS
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EXAMPLE
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480 is a term since A162296(480) = 1440 = 3*480.
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MATHEMATICA
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q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) == 3*n]; Select[Range[2, 10^7], q]
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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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