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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.

%I A356553 #9 Sep 19 2022 07:23:21
%S A356553 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,
%T A356553 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,
%U A356553 3,10,1,2,1,2,5,4,7,6,1,2,3,2,1,3,5,2,3
%N 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.
%C A356553 See A356552 for the corresponding bases.
%H A356553 Amiram Eldar, <a href="/A356553/b356553.txt">Table of n, a(n) for n = 1..10000</a>
%e A356553 For n = 14:
%e A356553 - we have:
%e A356553       b   sum of digits  divides 14?
%e A356553       --  -------------  -----------
%e A356553        2              3  no
%e A356553        3              4  no
%e A356553        4              5  no
%e A356553        5              6  no
%e A356553        6              4  no
%e A356553        7              2  yes
%e A356553 - so a(14) = 2.
%t A356553 a[n_] := Module[{b = 2}, While[!Divisible[n, (s = Plus @@ IntegerDigits[n, b])], b++]; s]; Array[a, 100] (* _Amiram Eldar_, Sep 19 2022 *)
%o A356553 (PARI) a(n) = { for (b=2, oo, my (s=sumdigits(n, b)); if (n % s==0, return (s))) }
%o A356553 (Python)
%o A356553 from sympy.ntheory import digits
%o A356553 def a(n):
%o A356553     b = 2
%o A356553     while n != 0 and n%sum(digits(n, b)[1:]): b += 1
%o A356553     return sum(digits(n, b)[1:])
%o A356553 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Aug 12 2022
%Y A356553 Cf. A356552.
%K A356553 nonn,base
%O A356553 1,6
%A A356553 _Rémy Sigrist_, Aug 12 2022