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A356552 a(n) is the least base b > 1 where the sum of digits of n divides n.

%I A356552 #11 Sep 19 2022 07:23:24
%S A356552 2,2,3,2,5,2,7,2,3,2,11,2,13,7,3,2,17,2,19,2,2,11,23,2,3,5,3,3,29,3,
%T A356552 31,2,3,2,3,2,37,19,3,2,41,2,43,6,3,23,47,2,7,4,5,4,53,3,2,3,3,29,59,
%U A356552 2,61,31,3,2,3,2,67,2,2,6,71,2,73,37,3,4,3,3,79
%N A356552 a(n) is the least base b > 1 where the sum of digits of n divides n.
%C A356552 This sequence is well defined: a(1) = 2, and for n > 1, the sum of digits of n in base n equals 1, which divides n.
%C A356552 See A356553 for the corresponding sum of digits.
%H A356552 Amiram Eldar, <a href="/A356552/b356552.txt">Table of n, a(n) for n = 1..10000</a>
%F A356552 a(n) = 2 iff n belongs to A049445.
%F A356552 a(n) = n iff n is prime.
%e A356552 For n = 14:
%e A356552 - we have:
%e A356552       b   sum of digits  divides 14?
%e A356552       --  -------------  -----------
%e A356552        2              3  no
%e A356552        3              4  no
%e A356552        4              5  no
%e A356552        5              6  no
%e A356552        6              4  no
%e A356552        7              2  yes
%e A356552 - so a(14) = 7.
%t A356552 a[n_] := Module[{b = 2}, While[!Divisible[n, Plus @@ IntegerDigits[n, b]], b++]; b]; Array[a, 100] (* _Amiram Eldar_, Aug 15 2022 *)
%o A356552 (PARI) a(n) = { for (b=2, oo, if (n % sumdigits(n, b)==0, return (b))) }
%o A356552 (Python)
%o A356552 from sympy.ntheory import digits
%o A356552 def a(n):
%o A356552     b = 2
%o A356552     while n != 0 and n%sum(digits(n, b)[1:]): b += 1
%o A356552     return b
%o A356552 print([a(n) for n in range(1, 80)]) # _Michael S. Branicky_, Aug 12 2022
%Y A356552 Cf. A049445, A356553.
%K A356552 nonn,base
%O A356552 1,1
%A A356552 _Rémy Sigrist_, Aug 12 2022