A356553 - OEIS

%I #9 Sep 19 2022 07:23:21

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

%N 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 See A356552 for the corresponding bases.

%H Amiram Eldar, <a href="/A356553/b356553.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 14:

%e - we have:

%e       b   sum of digits  divides 14?

%e       --  -------------  -----------

%e        2              3  no

%e        3              4  no

%e        4              5  no

%e        5              6  no

%e        6              4  no

%e        7              2  yes

%e - so a(14) = 2.

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

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

%o (Python)

%o from sympy.ntheory import digits

%o def a(n):

%o     b = 2

%o     while n != 0 and n%sum(digits(n, b)[1:]): b += 1

%o     return sum(digits(n, b)[1:])

%o print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Aug 12 2022

%Y Cf. A356552.

%K nonn,base

%O 1,6

%A _Rémy Sigrist_, Aug 12 2022