A098128 Perfect powers whose products of nonzero digits are also perfect powers.

1, 4, 8, 9, 49, 81, 100, 128, 144, 289, 343, 400, 441, 484, 841, 900, 1000, 1024, 1331, 1444, 2048, 2209, 2401, 2809, 3249, 3364, 4096, 4900, 7744, 8000, 8100, 8192, 8281, 8649, 9409, 9604, 10000, 10404, 11236, 11449, 11664, 11881, 13689, 13924, 14400, 14884, 16384, 16641

Offset

1,2

Links

Table of n, a(n) for n=1..48.

Example

484 is in the sequence because 22^2 = 484 and 4*8*4 = 128 = 2^7.

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *)
Select[Range[17000], perfectPowerQ[#] && perfectPowerQ[Times@@ DeleteCases[IntegerDigits[#], 0]] &] (* Stefano Spezia, Jun 27 2025 *)

Crossrefs

Cf. A001597.

Sequence in context: A385401 A239520 A083807 * A217700 A118895 A327654

Adjacent sequences: A098125 A098126 A098127 * A098129 A098130 A098131

Keyword

base,nonn

Author

Jason Earls, Sep 26 2004

Extensions

Missing powers of 10 inserted by Stefano Spezia, Jun 27 2025

Status

approved