A117689 Cubes for which the product of the digits is a square.

0, 1, 343, 1000, 1331, 4096, 8000, 10648, 19683, 27000, 39304, 50653, 64000, 74088, 79507, 103823, 110592, 125000, 140608, 148877, 205379, 216000, 238328, 250047, 300763, 328509, 343000, 389017, 405224, 493039, 512000, 551368, 592704, 636056

Offset

0,3

Comments

Any cube with a zero digit is a term of this sequence. Of the first 10,000 terms, only 331 have no zero digits. The largest such zero-free cube in the first 10,000 terms is 2956841564977. - Harvey P. Dale, Aug 22 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 0..10000

Example

19683 is in the sequence because it is a cube and the product of its digits 1*9*6*8*3=1296 is a square.

Mathematica

Select[Range[0, 100]^3, IntegerQ[Sqrt[Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Aug 22 2021 *)

Crossrefs

Cf. A000290, A000578.

Sequence in context: A336354 A269346 A202852 * A178374 A179147 A047739

Adjacent sequences: A117686 A117687 A117688 * A117690 A117691 A117692

Keyword

nonn,base

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 12 2006

Status

approved