Consecutive Odd Powerful Numbers

Theorem

$25$ and $27$ are the only known pair of consecutive odd powerful numbers.

It is not known whether there are any more.

Progress

We have that:

$25 = 5^2$

$27 = 3^3$

and so by definition both are powerful.

Sources

• 1970: Solomon W. Golomb: Powerful Numbers (Amer. Math. Monthly Vol. 77: pp. 848 – 855)  www.jstor.org/stable/2317020

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25$