A381825Odd cubefull exponentially odd numbers: numbers whose prime factorization has only odd primes and odd exponents that are larger than 1 (except for 1 whose prime factorization is empty).

1, 27, 125, 243, 343, 1331, 2187, 2197, 3125, 3375, 4913, 6859, 9261, 12167, 16807, 19683, …

The first 3 terms appear at position 1,485,230.

…332810494710097653886108127125966994734619791133838764…
position 1,485,230
termsstringfirst positionoccurrences
11199,997,334
21272971,000,569
31271251,485,2301,008
4127125243not within 1,000,000,0000
5127125243343not within 1,000,000,0000

Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.