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URL: https://oeis.org/A064700

⇱ A064700 - OEIS

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A064700
Numbers k that are divisible by the multiplicative digital root of k.
4
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.
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
-- Reinhard Zumkeller, Sep 22 2011
CROSSREFS
KEYWORD
nonn,base,nice
AUTHOR
Santi Spadaro, Oct 12 2001
STATUS
approved