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a(n) is the least multiple of n that is a Niven (or Harshad) number.
2

%I #12 Oct 22 2022 09:51:04

%S 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 50,156,27,84,261,30,372,192,132,102,70,36,111,114,117,40,410,42,516,

%U 132,45,230,423,48,392,50,102,156,954,54,110,112,114,522,531,60

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

%C Niven (or Harshad) numbers are divisible by the sum of their digits, and correspond to sequence A005349.

%H Rémy Sigrist, <a href="/A357936/b357936.txt">Table of n, a(n) for n = 1..10000</a>

%H David Radcliffe, <a href="/A144261/a144261.pdf">Every positive integer divides a Harshad number</a>

%H <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>

%F a(n) = n * A144261(n).

%e For n = 67, we have:

%e .

%e k 67*k Niven?

%e - ---- ------

%e 1 67 No

%e 2 134 No

%e 3 201 Yes

%e so a(67) = 201.

%t a[n_]:=Module[{k=1}, While[!Divisible[k*n, Total[IntegerDigits[k*n]]], k++]; k*n]; Array[a, 60]

%o (PARI) a(n, base=10) = forstep (m=n, oo, n, if (m%sumdigits(m, base)==0, return (m)))

%Y Cf. A005349, A144261, A357937.

%K nonn,base,easy

%O 1,2

%A _Rémy Sigrist_, Oct 21 2022