A344487 a(n) is the least k such that n is divisible by the sum of digits of k and k is divisible by the sum of digits of n; a(n) = -1 if no such k exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 3, 76, 10, 12, 35, 296, 9, 10, 2, 3, 20, 10, 6, 14, 184, 9, 10, 20999, 3, 100, 10, 12, 98, 16, 9, 10, 11, 12, 4, 10, 6, 99799, 40, 9, 10, 2099999, 12, 52, 5, 12, 49, 1000, 9, 10, 11, 12, 1001, 7998998, 6, 7999999, 200, 9, 10

Offset: 1

Author

Rémy Sigrist, May 21 2021

Keywords

• nonn
• base

Comments

Is a(n) > 0 for every n?

Examples

			For n = 15:
- the sum of digits of 15 is 6,
- so a(15) must be a multiple of 6,
- the sum of digits of 6 is 6, and 6 does not divide 15,
- the sum of digits of 12 is 3, and 3 divides 15,
- so a(15) = 12.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..500
• Rémy Sigrist, PARI program for A344487

Crossrefs

Cf. A005349, A007953, A344486.

Programs

PARI

See Links section.