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

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 110, 12, 117, 42, 30, 48, 102, 18, 114, 20, 21, 110, 207, 24, 50, 156, 27, 84, 261, 30, 372, 192, 132, 102, 70, 36, 111, 114, 117, 40, 410, 42, 516, 132, 45, 230, 423, 48, 392, 50, 102, 156, 954, 54, 110, 112, 114, 522, 531, 60

Offset

1,2

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

David Radcliffe, Every positive integer divides a Harshad number

Index entries for sequences related to decimal expansion of n

Formula

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

Example

For n = 67, we have:
.
      k  67*k  Niven?
      -  ----  ------
      1    67  No
      2   134  No
      3   201  Yes
so a(67) = 201.

Mathematica

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

Prog

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

Crossrefs

Cf. A005349, A144261, A357937.

Sequence in context: A071274 A258373 A250266 * A085908 A376280 A110304

Adjacent sequences: A357933 A357934 A357935 * A357937 A357938 A357939

Keyword

nonn,base,easy

Author

Rémy Sigrist, Oct 21 2022

Status

approved