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A357937 a(n) is the least multiple of n that is not a Niven (or Harshad) number.

%I A357937 #9 Oct 22 2022 09:51:08
%S A357937 11,14,15,16,15,66,14,16,99,130,11,96,13,14,15,16,17,2898,19,160,105,
%T A357937 22,23,96,25,26,189,28,29,390,31,32,33,34,35,2988,37,38,39,160,41,168,
%U A357937 43,44,495,46,47,96,49,250,51,52,53,28998,55,56,57,58,59,4980,61
%N A357937 a(n) is the least multiple of n that is not a Niven (or Harshad) number.
%C A357937 Niven (or Harshad) numbers are divisible by the sum of their digits, and correspond to sequence A005349.
%H A357937 Rémy Sigrist, <a href="/A357937/b357937.txt">Table of n, a(n) for n = 1..10000</a>
%H A357937 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%F A357937 a(n) = n * A144262(n).
%e A357937 For n = 3, we have:
%e A357937 .
%e A357937       k  3*k  Niven?
%e A357937       -  ---  ------
%e A357937       1    3  Yes
%e A357937       2    6  Yes
%e A357937       3    9  Yes
%e A357937       4   12  Yes
%e A357937       5   15  No
%e A357937 so a(3) = 15.
%t A357937 a[n_]:=Module[{k=1}, While[Divisible[k*n, Total[IntegerDigits[k*n]]], k++]; k*n]; Array[a, 61]
%o A357937 (PARI) a(n, base=10) = forstep (m=n, oo, n, if (m%sumdigits(m, base), return (m)))
%Y A357937 Cf. A005349, A144262, A357936.
%K A357937 nonn,base
%O A357937 1,1
%A A357937 _Rémy Sigrist_, Oct 21 2022