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.

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

Offset

1,6

Comments

See A356552 for the corresponding bases.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

For n = 14:
- we have:
      b   sum of digits  divides 14?
      --  -------------  -----------
       2              3  no
       3              4  no
       4              5  no
       5              6  no
       6              4  no
       7              2  yes
- so a(14) = 2.

Mathematica

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

Prog

(PARI) a(n) = { for (b=2, oo, my (s=sumdigits(n, b)); if (n % s==0, return (s))) }
(Python)
from sympy.ntheory import digits
def a(n):
    b = 2
    while n != 0 and n%sum(digits(n, b)[1:]): b += 1
    return sum(digits(n, b)[1:])
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Aug 12 2022

Crossrefs

Cf. A356552.

Sequence in context: A076820 A206824 A293810 * A324369 A276781 A303759

Adjacent sequences: A356550 A356551 A356552 * A356554 A356555 A356556

Keyword

nonn,base

Author

Rémy Sigrist, Aug 12 2022

Status

approved