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A118694
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Semiprimes which are divisible by the product of their digits.
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2
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4, 6, 9, 15, 111, 115, 1111, 1115, 11111, 1111111, 1111117, 111111115, 1111113111, 1111711111, 11111111111, 111111111115, 1111111111113, 1111117111111, 11171111111111, 1111111111711111, 1111711111111111, 11111111111111111
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OFFSET
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1,1
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COMMENTS
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The Mathematica coding is only good for multidigital, nonrepunits numbers. Obviously 4, 6 and 9 are members and so are A102782: Repunit semiprimes. - Robert G. Wilson v, Jun 10 2006
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LINKS
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FORMULA
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EXAMPLE
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115 is in the sequence because (1) it is a semiprime, (2) the product of its digits is 1*1*5=5 and (3) 115 is divisible by 5.
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MAPLE
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sp:= proc(n) evalb(2=add (i[2], i=ifactors(n) [2])) end: dp:= proc(n) local m; m:=n; 1; while m<>0 do %*irem(m, 10, 'm') od; % end: select(x-> irem(x, dp(x))=0 and sp(x), sort([{4, 6, 9, seq(seq(seq(parse(cat(1$(k-j), t, 1$j)), j=0..k), t=[1, 3, 5, 7]), k=1..20)} []]))[]; # Alois P. Heinz, Nov 17 2009
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MATHEMATICA
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lst = {}; Do[ p = Times @@ IntegerDigits@n; If[ PrimeQ@p && PrimeQ[n/p], AppendTo[lst, n]; Print[n]], {n, 275*10^6}]; lst (* Robert G. Wilson v, Jun 10 2006 *)
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PROG
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(PARI) A007954(n)= { local(resul, ncpy); if(n<10, return(n) ); ncpy=n; resul = ncpy % 10; ncpy = (ncpy - ncpy%10)/10; while( ncpy > 0, resul *= ncpy %10; ncpy = (ncpy - ncpy%10)/10; ); return(resul); } { for(n=4, 50000000, if( bigomega(n)==2, dr=A007954(n); if(dr !=0 && n % dr == 0, print1(n, ", "); ); ); ); } \\ R. J. Mathar, May 23 2006
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), May 20 2006
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EXTENSIONS
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STATUS
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approved
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