A118694 - OEIS

%I #16 Aug 22 2015 19:58:23

%S 4,6,9,15,111,115,1111,1115,11111,1111111,1111117,111111115,

%T 1111113111,1111711111,11111111111,111111111115,1111111111113,

%U 1111117111111,11171111111111,1111111111711111,1111711111111111,11111111111111111

%N Semiprimes which are divisible by the product of their digits.

%C 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

%H Alois P. Heinz, <a href="/A118694/b118694.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = A001358(k): A007954(a(n)) | a(n). - _R. J. Mathar_, May 23 2006

%e 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.

%p 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

%t 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 *)

%o (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

%Y Cf. A001358, A102782, A046413, A118693.

%K base,nonn

%O 1,1

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

%E More terms from _R. J. Mathar_, May 23 2006

%E a(12) from _Robert G. Wilson v_, Jun 10 2006

%E Further terms from _Alois P. Heinz_, Nov 17 2009