A061430 Geometric mean of the digits is an integer: k-digit numbers such that the product of the digits is a number of the form m^k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 20, 22, 28, 30, 33, 40, 41, 44, 49, 50, 55, 60, 66, 70, 77, 80, 82, 88, 90, 91, 94, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 118, 120, 124, 130, 139, 140, 142, 150, 160, 170, 180, 181, 188, 190, 193

Offset: 1

Author

Amarnath Murthy, May 03 2001

Keywords

• nonn
• base
• easy
• nice

Examples

			694 is a term as (6*9*4)^(1/3) = 6 is an integer.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..5000

Crossrefs

Cf. A061426, A061427, A061428.

Programs

Haskell

a061430 n = a061430_list !! (n-1)
a061430_list = filter g [0..] where
   g u = round (fromIntegral p ** (1 / fromIntegral k)) ^ k == p where
         (p, k) = h (1, 0) u
         h (p, l) 0 = (p, l)
         h (p, l) v = h (p * r, l + 1) v' where (v', r) = divMod v 10
-- Reinhard Zumkeller, Jan 13 2014

Mathematica

Select[Range[0,200],IntegerQ[GeometricMean[IntegerDigits[#]]]&] (* Harvey P. Dale, Feb 15 2012 *)

Extensions

More terms from Naohiro Nomoto, May 11 2001