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

11, 14, 15, 16, 15, 66, 14, 16, 99, 130, 11, 96, 13, 14, 15, 16, 17, 2898, 19, 160, 105, 22, 23, 96, 25, 26, 189, 28, 29, 390, 31, 32, 33, 34, 35, 2988, 37, 38, 39, 160, 41, 168, 43, 44, 495, 46, 47, 96, 49, 250, 51, 52, 53, 28998, 55, 56, 57, 58, 59, 4980, 61

Offset

1,1

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

Index entries for sequences related to decimal expansion of n

Formula

a(n) = n * A144262(n).

Example

For n = 3, we have:
.
      k  3*k  Niven?
      -  ---  ------
      1    3  Yes
      2    6  Yes
      3    9  Yes
      4   12  Yes
      5   15  No
so a(3) = 15.

Mathematica

a[n_]:=Module[{k=1}, While[Divisible[k*n, Total[IntegerDigits[k*n]]], k++]; k*n]; Array[a, 61]

Prog

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

Crossrefs

Cf. A005349, A144262, A357936.

Sequence in context: A083124 A132991 A031167 * A005788 A091403 A061743

Adjacent sequences: A357934 A357935 A357936 * A357938 A357939 A357940

Keyword

nonn,base

Author

Rémy Sigrist, Oct 21 2022

Status

approved