A066565 Numbers that when multiplied by the product of their nonzero digits produce a square.

1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 45, 49, 96, 98, 100, 135, 144, 200, 250, 288, 289, 300, 338, 378, 384, 400, 405, 441, 500, 600, 700, 800, 882, 900, 1444, 1445, 1575, 1715, 1800, 2205, 2209, 2744, 2809, 3703, 4418, 4500, 4900, 5290, 6144, 6912, 6962, 7560, 7623

Offset: 1

Author

Amarnath Murthy, Dec 18 2001

Keywords

• base
• nonn

Examples

			45 is a member as 45*4*5 = 900 = 30^2; 135 is a member as 135*3*5 = 2025 = 45^2; 200 is a member as 200*2 = 400.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A051801.

Programs

PARI

isok(k) = issquare( k * vecprod(select(x->(x!=0), digits(k))) )

Extensions

More terms from Jason Earls, Dec 24 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 04 2010