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

1,3

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).

Links

Table of n, a(n) for n=1..44.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Sequence A053059 removes the numbers with zeros.

Sequence in context: A055812 A368337 A268099 * A019544 A053059 A006716

Adjacent sequences: A061864 A061865 A061866 * A061868 A061869 A061870

Keyword

base,easy,nonn

Author

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

Status

approved