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

Author

Rémy Sigrist, Oct 21 2022

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

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

Crossrefs

Cf. A005349, A144261, A357937.

Programs

Mathematica

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

PARI

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

Formula

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