A066565 Numbers that when successively multiplied by 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

1,2

Links

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

Example

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.

Prog

(PARI):a066565(a, b) = local(n, s, d, q); for(n=a, b, s=1; q=n; while(q>0, d=divrem(q, 10); q=d[1]; s=s*max(1, d[2])); if(issquare(n*s), print1(n, ", "))) a066565(1, 20000)
(PARI) ProdNzD(x)= { local(d, p=1); while (x>9, d=x%10; if (d, p*=d); x\=10); return(p*x) } { n=0; for (m=1, 10^10, if (issquare(m*ProdNzD(m)), write("b066565.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 04 2010

Crossrefs

Sequence in context: A032944 A273736 A048409 * A095966 A180084 A092596

Adjacent sequences: A066562 A066563 A066564 * A066566 A066567 A066568

Keyword

base,nonn

Author

Amarnath Murthy, Dec 18 2001

Extensions

More terms from Jason Earls, Dec 24 2001

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

Status

approved