Abundant Squares

Number Theory Level 4

Find the sum of first three abundant numbers which are perfect squares?

Details and Assumptions

A number $n$ is called Abundant Number if $\sigma(n)>2n$ .

2 solutions

Kalpok Guha
Apr 2, 2015

The numbers in the form $p^k$ are always deficient.

So the square of primes cannot be abundant. We start with numbers which have four divisors.

First the square of $6$ we got it $(36)$ abundant. Then $10^2,12^2$ are also abundant.

$8^2$ did n’t satisfied the condition as it is in the form $p^k$ .

Thus the answer is $36+100+144=280$

Sai Ram
Jul 17, 2015

https://oeis.org/A005101