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A066565
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Numbers which when successively multiplied by their nonzero digits produce a square.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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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.
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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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 04 2010]
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CROSSREFS
| Sequence in context: A108690 A032944 A048409 * A095966 A180084 A092596
Adjacent sequences: A066562 A066563 A066564 * A066566 A066567 A066568
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KEYWORD
| base,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 18 2001
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EXTENSIONS
| More terms from Jason Earls (zevi_35711(AT)yahoo.com), Dec 24 2001
OFFSET changed from 0,2 to 1,2 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 04 2010
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