A357866 a(n) is the greatest remainder of n divided by its sum of digits in any base > 1.

0, 0, 1, 0, 2, 0, 3, 2, 4, 2, 5, 2, 6, 4, 7, 4, 8, 4, 9, 6, 10, 6, 11, 6, 12, 8, 13, 8, 14, 8, 15, 10, 16, 10, 17, 10, 18, 12, 19, 12, 20, 12, 21, 14, 22, 14, 23, 14, 24, 16, 25, 16, 26, 16, 27, 18, 28, 18, 29, 18, 30, 20, 31, 20, 32, 20, 33, 22, 34, 22, 35

Offset: 1

Author

Rémy Sigrist, Oct 17 2022

Keywords

• nonn
• base

Examples

			For n = 11, we have:
       b  sum of digits  remainder
    ----  -------------  ---------
       2              3          2
       3              3          2
       4              5          1
       5              3          2
       6              6          5
       7              5          1
       8              4          3
       9              3          2
      10              2          1
      11              1          0
    >=12             11          0
so a(11) = 5.
		

Crossrefs

Cf. A138530, A357823.

Programs

PARI

a(n) = { my (mx=0); for (b=2, n, mx=max(mx, n%sumdigits(n, b))); return (mx); }

Python

from sympy.ntheory import digits
def a(n): return max((n%sum(digits(n, b)[1:]) for b in range(2, n+1)), default=0)
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Oct 17 2022