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%I #16 Feb 27 2024 19:37:45
%S 4,6,9,15,26,34,35,62,111,115,134,278,314,355,395,398,535,694,755,
%T 1111,1115,1126,1135,1315,1322,1355,1535,1795,2962,3155,3338,3662,
%U 3898,3994,4174,4714,5315,6166,6326,6334,6362,6686,6866,6914,6922,7115,7195,7915
%N Semiprimes which are divisible by their multiplicative digital root.
%H Amiram Eldar, <a href="/A118696/b118696.txt">Table of n, a(n) for n = 1..10000</a>
%e 134 is in the sequence because it is a semiprime and it is divisible by its multiplicative digital root, 2.
%t spQ[n_] := Plus @@ Last /@ FactorInteger@n == 2; mdrQ[n_] := Mod[n, NestWhile[Times @@ IntegerDigits@# &, n, UnsameQ, All]] == 0; Select[ Range@9754, spQ@# && mdrQ@# &] (* _Robert G. Wilson v_, Aug 04 2006 *)
%t mdr[n_]:=Module[{c=NestWhile[Times@@IntegerDigits[#]&,n,#>9&]},If[c>0,c,Pi]]; Select[ Range[ 8000],PrimeOmega[#]==2&&Divisible[#,mdr[#]]&] (* _Harvey P. Dale_, Feb 27 2024 *)
%o (PARI) A031347(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(A031347(resul)); } { for(n=4,5000, if( bigomega(n)==2, dr=A031347(n); if(dr !=0 && n % dr == 0, print1(n,","); ); ); ); } \\ _R. J. Mathar_, May 23 2006
%Y Intersection of A001358 and A064700.
%K base,nonn
%O 1,1
%A Luc Stevens (lms022(AT)yahoo.com), May 20 2006
%E Corrected by _R. J. Mathar_, May 23 2006
%E More terms from _Robert G. Wilson v_, Aug 04 2006
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