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

%I A357866 #10 Oct 21 2022 06:59:29
%S A357866 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,
%T A357866 10,16,10,17,10,18,12,19,12,20,12,21,14,22,14,23,14,24,16,25,16,26,16,
%U A357866 27,18,28,18,29,18,30,20,31,20,32,20,33,22,34,22,35
%N A357866 a(n) is the greatest remainder of n divided by its sum of digits in any base > 1.
%e A357866 For n = 11, we have:
%e A357866        b  sum of digits  remainder
%e A357866     ----  -------------  ---------
%e A357866        2              3          2
%e A357866        3              3          2
%e A357866        4              5          1
%e A357866        5              3          2
%e A357866        6              6          5
%e A357866        7              5          1
%e A357866        8              4          3
%e A357866        9              3          2
%e A357866       10              2          1
%e A357866       11              1          0
%e A357866     >=12             11          0
%e A357866 so a(11) = 5.
%o A357866 (PARI) a(n) = { my (mx=0); for (b=2, n, mx=max(mx, n%sumdigits(n, b))); return (mx); }
%o A357866 (Python)
%o A357866 from sympy.ntheory import digits
%o A357866 def a(n): return max((n%sum(digits(n, b)[1:]) for b in range(2, n+1)), default=0)
%o A357866 print([a(n) for n in range(1, 72)]) # _Michael S. Branicky_, Oct 17 2022
%Y A357866 Cf. A138530, A357823.
%K A357866 nonn,base
%O A357866 1,5
%A A357866 _Rémy Sigrist_, Oct 17 2022