A356553 For any n > 0, let b > 1 be the least base where the sum of digits of n divides n; a(n) is the sum of digits of n in base b.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 2, 1, 2, 5, 2, 1, 2, 1, 2, 1, 1, 3, 2, 5, 2, 1, 2, 3, 2, 1, 3, 1, 4, 3, 2, 1, 2, 1, 5, 3, 4, 1, 2, 5, 4, 3, 2, 1, 4, 1, 2, 3, 1, 5, 2, 1, 2, 3, 10, 1, 2, 1, 2, 5, 4, 7, 6, 1, 2, 3, 2, 1, 3, 5, 2, 3

Offset: 1

Author

Rémy Sigrist, Aug 12 2022

Keywords

• nonn
• base

Comments

See A356552 for the corresponding bases.

Examples

			For n = 14:
- we have:
      b   sum of digits  divides 14?
      --  -------------  -----------
       2              3  no
       3              4  no
       4              5  no
       5              6  no
       6              4  no
       7              2  yes
- so a(14) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A356552.

Programs

Mathematica

a[n_] := Module[{b = 2}, While[!Divisible[n, (s = Plus @@ IntegerDigits[n, b])], b++]; s]; Array[a, 100] (* Amiram Eldar, Sep 19 2022 *)

PARI

a(n) = { for (b=2, oo, my (s=sumdigits(n, b)); if (n % s==0, return (s))) }

Python

from sympy.ntheory import digits
def a(n):
    b = 2
    while n != 0 and n%sum(digits(n, b)[1:]): b += 1
    return sum(digits(n, b)[1:])
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Aug 12 2022