login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Semiprimes which are divisible by their multiplicative digital root.
1

%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