A064700 - OEIS

%I #25 Sep 04 2023 11:12:10

%S 1,2,3,4,5,6,7,8,9,11,12,15,24,26,34,35,48,62,64,72,75,84,88,111,112,

%T 115,126,132,134,135,136,144,162,168,172,174,175,176,186,192,212,216,

%U 228,232,246,248,264,276,278,282,288,312,314,315,322,355,364,376,378

%N Numbers k that are divisible by the multiplicative digital root of k.

%C No term has 0 as one of its digits.

%C The only primes in the sequence are {2, 3, 5, 7, 11} and any other prime that has only 1s as digits, such as 1111111111111111111.

%H Reinhard Zumkeller, <a href="/A064700/b064700.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.

%t mdr[n_] := FixedPoint[ Times @@ IntegerDigits[#] &, n]; Select[ Range[400], (m = mdr[#]; m > 0 && Mod[#, m] == 0) &] (* _Jean-François Alcover_, Nov 30 2011 *)

%t dvsbQ[n_]:=Mod[n,NestWhile[Times@@IntegerDigits[#]&,n,#>9&]/.(0->Pi)]==0; Select[Range[ 500], dvsbQ] (* _Harvey P. Dale_, Aug 09 2023 *)

%o (Haskell)

%o a064700 n = a064700_list !! (n-1)

%o a064700_list = filter f [1..] where

%o    f x = mdr > 0 && x `mod` mdr == 0 where mdr = a031347 x

%o -- Reinhad Zumkeller, Sep 22 2011

%Y Cf. A031346, A007954, A031347, A052382.

%K nonn,base,nice

%O 1,2

%A _Santi Spadaro_, Oct 12 2001