A356552 a(n) is the least base b > 1 where the sum of digits of n divides n.
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, 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, 2, 61, 31, 3, 2, 3, 2, 67, 2, 2, 6, 71, 2, 73, 37, 3, 4, 3, 3, 79
Offset: 1
Examples
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) = 7.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
a[n_] := Module[{b = 2}, While[!Divisible[n, Plus @@ IntegerDigits[n, b]], b++]; b]; Array[a, 100] (* Amiram Eldar, Aug 15 2022 *) -
PARI
a(n) = { for (b=2, oo, if (n % sumdigits(n, b)==0, return (b))) } -
Python
from sympy.ntheory import digits def a(n): b = 2 while n != 0 and n%sum(digits(n, b)[1:]): b += 1 return b print([a(n) for n in range(1, 80)]) # Michael S. Branicky, Aug 12 2022
Formula
a(n) = 2 iff n belongs to A049445.
a(n) = n iff n is prime.
Comments