OFFSET
1,1
COMMENTS
The first case (130) yields a number divisible by 83^2. The next 5 terms yield numbers divisible by 59^2. Boyd et al. are not completely certain about the other 994 numbers up to 1000. They conjecture that 0.9934466... of numbers n^n + (-1)^n (n-1)^(n-1) are squarefree.
Boyd et al. tested the values n <= 1000 for divisibility by the squares of the first 10^4 primes. To extend the sequence, I tested the divisibility of n <= 200000 by the squares of the first 10^5 primes. - Giovanni Resta, Feb 24 2014
The heuristic chance that Resta's list is incomplete is just over 1%. This drops to 0.07% with testing to the millionth prime. - Charles R Greathouse IV, Feb 25 2014
LINKS
David W. Boyd, Greg Martin, and Mark Thom, Squarefree values of trinomial discriminants, arXiv 1402.5148 [math.NT], 2014.
Chandrashekhar Khare, Alfio Fabio La Rosa, and Gabor Wiese, Splitting fields of X^n - X - 1 (particularly for n = 5), prime decomposition and modular forms, Univ. du Luxembourg (2022).
Giovanni Resta, Terms < 200000 and corresponding square divisors
PROG
(PARI) is(n)=!issquarefree(n^n + (-1)^n*(n-1)^(n-1)) \\ Charles R Greathouse IV, Feb 25 2014
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
T. D. Noe, Feb 24 2014
EXTENSIONS
a(7)-a(44) from Giovanni Resta, Feb 24 2014
STATUS
approved