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A357936 a(n) is the least multiple of n that is a Niven (or Harshad) number.

%I A357936 #12 Oct 22 2022 09:51:04
%S A357936 1,2,3,4,5,6,7,8,9,10,110,12,117,42,30,48,102,18,114,20,21,110,207,24,
%T A357936 50,156,27,84,261,30,372,192,132,102,70,36,111,114,117,40,410,42,516,
%U A357936 132,45,230,423,48,392,50,102,156,954,54,110,112,114,522,531,60
%N A357936 a(n) is the least multiple of n that is a Niven (or Harshad) number.
%C A357936 Niven (or Harshad) numbers are divisible by the sum of their digits, and correspond to sequence A005349.
%H A357936 Rémy Sigrist, <a href="/A357936/b357936.txt">Table of n, a(n) for n = 1..10000</a>
%H A357936 David Radcliffe, <a href="/A144261/a144261.pdf">Every positive integer divides a Harshad number</a>
%H A357936 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%F A357936 a(n) = n * A144261(n).
%e A357936 For n = 67, we have:
%e A357936 .
%e A357936       k  67*k  Niven?
%e A357936       -  ----  ------
%e A357936       1    67  No
%e A357936       2   134  No
%e A357936       3   201  Yes
%e A357936 so a(67) = 201.
%t A357936 a[n_]:=Module[{k=1}, While[!Divisible[k*n, Total[IntegerDigits[k*n]]], k++]; k*n]; Array[a, 60]
%o A357936 (PARI) a(n, base=10) = forstep (m=n, oo, n, if (m%sumdigits(m, base)==0, return (m)))
%Y A357936 Cf. A005349, A144261, A357937.
%K A357936 nonn,base,easy
%O A357936 1,2
%A A357936 _Rémy Sigrist_, Oct 21 2022