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

1,2

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.

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 *)

Prog

(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

Crossrefs

Cf. A031346, A007954, A031347, A052382.

Sequence in context: A209933 A182183 A308472 * A180484 A007602 A343681

Adjacent sequences: A064697 A064698 A064699 * A064701 A064702 A064703

Keyword

nonn,base,nice

Author

Santi Spadaro, Oct 12 2001

Status

approved