A118696 Semiprimes which are divisible by their multiplicative digital root.

4, 6, 9, 15, 26, 34, 35, 62, 111, 115, 134, 278, 314, 355, 395, 398, 535, 694, 755, 1111, 1115, 1126, 1135, 1315, 1322, 1355, 1535, 1795, 2962, 3155, 3338, 3662, 3898, 3994, 4174, 4714, 5315, 6166, 6326, 6334, 6362, 6686, 6866, 6914, 6922, 7115, 7195, 7915

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

134 is in the sequence because it is a semiprime and it is divisible by its multiplicative digital root, 2.

Mathematica

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 *)
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 *)

Prog

(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

Crossrefs

Intersection of A001358 and A064700.

Sequence in context: A087718 A033476 A183978 * A065856 A136357 A136356

Adjacent sequences: A118693 A118694 A118695 * A118697 A118698 A118699

Keyword

base,nonn

Author

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

Extensions

Corrected by R. J. Mathar, May 23 2006

More terms from Robert G. Wilson v, Aug 04 2006

Status

approved