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A118694 Semiprimes which are divisible by the product of their digits. 2
4, 6, 9, 15, 111, 115, 1111, 1115, 11111, 1111111, 1111117, 111111115, 1111113111, 1111711111, 11111111111, 111111111115, 1111111111113, 1111117111111, 11171111111111, 1111111111711111, 1111711111111111, 11111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
a(n) = A001358(k): A007954(a(n)) | a(n). - R. J. Mathar, May 23 2006
EXAMPLE
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.
MAPLE
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A136356 A136358 A115665 * A085648 A300131 A045114
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), May 20 2006
EXTENSIONS
More terms from R. J. Mathar, May 23 2006
a(12) from Robert G. Wilson v, Jun 10 2006
Further terms from Alois P. Heinz, Nov 17 2009
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)