OFFSET
1,2
COMMENTS
k = 10^m is a term of the sequence for all m >= 0. Proof: Let k = 10^m for some nonnegative integer m. Then k^k - 1 has m*10^m 9's and no other digits, so its digits sum to 9*m*10^m = 9*m*k, a multiple of k.
EXAMPLE
The digits of 9775^9775 - 1 sum to 175950 and 175950 is divisible by 9775, so 9775 is in the sequence.
MAPLE
sumdigs:= n -> convert(convert(n, base, 10), `+`);
select(n -> sumdigs(n^n-1) mod n = 0, [$1..10^5]); # Robert Israel, Dec 03 2014
MATHEMATICA
Do[k = n^n - 1; s = Plus @@ IntegerDigits[k]; If[Mod[s, n] == 0, Print[n]], {n, 1, 10^5}]
PROG
(Python)
A109675_list = [n for n in range(1, 10**4) if not sum([int(d) for d in str(n**n-1)]) % n]
# Chai Wah Wu, Dec 03 2014
CROSSREFS
KEYWORD
base,hard,more,nonn
AUTHOR
Ryan Propper, Aug 06 2005
EXTENSIONS
a(13)-a(16) from Michael S. Branicky, Jun 25 2023
STATUS
approved