A118694 Semiprimes which are divisible by the product of their digits.

4, 6, 9, 15, 111, 115, 1111, 1115, 11111, 1111111, 1111117, 111111115, 1111113111, 1111711111, 11111111111, 111111111115, 1111111111113, 1111117111111, 11171111111111, 1111111111711111, 1111711111111111, 11111111111111111

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 20 2006

Keywords

• base
• nonn

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

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A001358, A102782, A046413, A118693.

Programs

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 *)

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

Formula

a(n) = A001358(k): A007954(a(n)) | a(n). - R. J. Mathar, May 23 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