Euler's Pentagonal Numbers Theorem/Corollary 1/Historical Note

Historical Note on Sigma of Integer equals Sum of Sequence of Sigma of Integers indexed by Generalized Pentagonal Numbers
had noticed, but had not formally proved, the result Generalized Pentagonal Numbers form Exponents of Infinite Product of $1 - x^n$.

However, he was so convinced of its truth that he used it to prove this and other results.

Hence he demonstrated the interesting fact that, in order to calculate the sum of the divisors of a number, it is necessary merely to know the sum of the divisors of the relevant smaller numbers, but not what those divisors themselves actually are.