Determine Superabundance

Jelly, 7 bytes

Æs÷$ÞṪ=

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Jelly, 8 bytes

Æs÷$ÐṀ⁼W

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Test Suite!

Explanation

Æs÷$ÐṀ⁼W ~ Full program (monadic).

    ÐṀ   ~ Keep the elements with maximal link value (auto-rangifies).
Æs       ~ Divisor sum.
  ÷$     ~ Divide by the current element.
      ⁼W ~ Check equality with the input wrapped into a singleton.
         ~ (for integers like 360360)

Haskell, 73 bytes

-1 byte thanks to Mr. Xcoder. -7 bytes thanks to Laikoni.

r=read.show
s n=sum[r i|i<-[1..n],n`mod`i<1]/r n
f n=all((s n>=).s)[1..n]

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Haskell's type system isn't very golfy...

Haskell, 64 63 61 bytes

-1 byte thanks to Mr. Xcoder.

-2 bytes thanks to Lynn.

a!x=a*sum[y|y<-[1..x],mod x y<1]
f n=and[x!n>n!x|x<-[1..n-1]]

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