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