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A118696
Semiprimes which are divisible by their multiplicative digital root.
1
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
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
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