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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.
2
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
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Aug 12 2022
STATUS
approved