A061867 Squares whose product of digits is also a square (allowing zeros).

0, 1, 4, 9, 49, 100, 144, 289, 400, 441, 900, 1024, 1089, 1444, 1600, 2025, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 3025, 3600, 4096, 4900, 5041, 6084, 6400, 7056, 7744, 8100, 9025, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10816, 11025, 11236

Offset: 1

Author

Larry Reeves (larryr(AT)acm.org), May 11 2001

Keywords

• base
• easy
• nonn

References

• Felice Russo, A set of new Smarandache Functions, Sequences and conjectures in number theory, pp-64, American Research Press, Lupton USA.
• Amarnath Murthy, Exploring some new ideas on Smarandache Type Sets, Functions and sequences, Vol. 11, No. 1-2-3, Spring 2000.
• Amarnath Murthy, On the infinitude of Smarandache multiplicative square sequence, (to be published in Smarandache Notions Journal).

Crossrefs

Sequence A053059 removes the numbers with zeros.

Programs

Mathematica

Select[Range[0,200]^2,IntegerQ[Sqrt[Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Oct 03 2014 *)

PARI

isok(n) = {if (! issquare(n), return (0)); digs = digits(n, 10); issquare(prod(i=1, #digs, digs[i]));}  \\ Michel Marcus, Aug 02 2013

Formula

a(n) ~ n^2. - Charles R Greathouse IV, Sep 19 2012