A064700 Numbers k that are divisible by the multiplicative digital root of k.

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, 115, 126, 132, 134, 135, 136, 144, 162, 168, 172, 174, 175, 176, 186, 192, 212, 216, 228, 232, 246, 248, 264, 276, 278, 282, 288, 312, 314, 315, 322, 355, 364, 376, 378

Offset: 1

Author

Santi Spadaro, Oct 12 2001

Keywords

• nonn
• base
• nice

Comments

No term has 0 as one of its digits.

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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A031346, A007954, A031347, A052382.

Programs

Haskell

a064700 n = a064700_list !! (n-1)
a064700_list = filter f [1..] where
   f x = mdr > 0 && x `mod` mdr == 0 where mdr = a031347 x
-- Reinhad Zumkeller, Sep 22 2011

Mathematica

mdr[n_] := FixedPoint[ Times @@ IntegerDigits[#] &, n]; Select[ Range[400], (m = mdr[#]; m > 0 && Mod[#, m] == 0) &] (* Jean-François Alcover, Nov 30 2011 *)
dvsbQ[n_]:=Mod[n,NestWhile[Times@@IntegerDigits[#]&,n,#>9&]/.(0->Pi)]==0; Select[Range[ 500], dvsbQ] (* Harvey P. Dale, Aug 09 2023 *)