OFFSET
1,2
COMMENTS
If n is a prime number, then a(n) has the form p^(n-1), where p is a prime number such that p <= 9 * ((n-1) * log_10(p) +1).
For p <= 9 * ((n-1) * log_10 (p) +1), if there is no s >= 1 such that digsum(p^(n-1)) = p^s, then a(n) = -1. For example, for n = 7, the largest prime number p verifying p <= 9 * (6 * log_10 (p) +1) is 113, but no prime number q <= 113 has the property digsum(q^6) = q^s, for 1 <= s <= 6. Thus, a(7) = -1.
EXAMPLE
The number 81 = 3^4 is the smallest with 5 divisors and is a Niven number, so a(5) = 81.
PROG
(Magma) niven:=func<n|n mod &+Intseq(n) eq 0 >; a:=[]; for n in [1..36] do if not IsPrime(n) then k:=1; while not niven(k) or #Divisors(k) ne n do k:=k+1; end while; Append(~a, k); else q:=2; while not niven(q^(n-1)) and q le (9*(n-1)*Log(10, q)+9) do q:=NextPrime(q); end while; if niven(q^(n-1)) then Append(~a, q^(n-1)); else Append(~a, -1); end if; end if; end for; a;
CROSSREFS
KEYWORD
sign,base
AUTHOR
Marius A. Burtea, Aug 04 2020
STATUS
approved