So Odd

Number Theory Level 3

Define f ( n ) f(n) is the sum of all positive divisors of n n (for example, f ( 6 ) = 1 + 2 + 3 + 6 = 12 f(6)=1+2+3+6=12 ), find the smallest odd n n such that f ( n ) > 2 n f(n) >2n .


The answer is 945.

X X by X X , 17, Taiwan

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2 solutions

Giorgos K.
Apr 24, 2018

Quick search using M a t h e m a t i c a Mathematica

Select[Range@1000,DivisorSigma[1,#]>2#&&OddQ@#&]

returns 945

here are some more...

945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8925, 9135, 9555, 9765 ...

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Theodore Sinclair
Apr 24, 2018

These are called abundant numbers and the first odd abundant number is 945 wiki abundant numbers see first bullet point of properties.

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