A393483 For k >= 1, perfect powers A001597(k) for which ratio A001597(k+1) / A001597(k) is smaller than that for any smaller k.

1, 4, 8, 25, 121, 125, 1728, 2025, 2187, 3125, 3364, 4900, 21904, 24336, 32761, 64000, 97336, 970225, 1030225, 1295029, 6436343, 14348907, 45118016, 75151448, 183250369, 199176704, 503284356, 2535525316, 18821096000, 28849701763, 141828313201, 143384152904

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Example

A001597(2)/A001597(1) = 4/1 = 4: a(1) = 1.
A001597(3)/A001597(2) = 8/4 = 2: a(2) = 4.
A001597(4)/A001597(3) = 9/8 = 1.125: a(3) = 8.
A001597(5)/A001597(4) = 16/9 = 1.777...: not smaller than the prevailing minimum.
A001597(6)/A001597(5) = 25/16 = 1.5625: not smaller than the prevailing minimum.
A001597(7)/A001597(6) = 27/25 = 1.08: a(4) = 25.

Prog

(PARI) my(r=oo, pprev=1); for(p=2, 10^10, if(!ispower(p), next); if(p/pprev<r, r=p/pprev; print1(pprev, ", ")); pprev=p)

Crossrefs

Cf. A001597.

Sequence in context: A046736 A174171 A262042 * A227644 A074188 A126733

Adjacent sequences: A393480 A393481 A393482 * A393485 A393486 A393487

Keyword

nonn

Author

Charles L. Hohn, Mar 27 2026

Status

approved