Smallest Odd Abundant Number not Divisible by 3

Theorem
The smallest odd abundant number not divisible by $3$ is $5 \, 391 \, 411 \, 025$.

Proof
We have:
 * $5 \, 391 \, 411 \, 025 = 5^2 \times 7 \times 11 \times 13 \times 17 \times 19 \times 23 \times 29$

showing it is not divisible by $3$.

Then from we have:
 * $\map {\sigma_1} {5 \, 391 \, 411 \, 025} = 10 \, 799 \, 308 \, 800 = 2 \times 5 \, 391 \, 411 \, 025 + 16 \, 486 \, 750$

demonstrating that $5 \, 391 \, 411 \, 025$ is abundant.