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 A238194 Conjectured numbers n for which n^n + (-1)^n (n-1)^(n-1) is not squarefree. 2
 130, 257, 487, 528, 815, 897, 1176, 1225, 1320, 1373, 1430, 2029, 2050, 2084, 2198, 2247, 2526, 2608, 2895, 2936, 2958, 3166, 3679, 3849, 3909, 3950, 4237, 4319, 4598, 4647, 4723, 4795, 5472, 5487, 5620, 5669, 5948, 6030, 6317, 6358, 6588, 6677, 6936, 7101 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..44. 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 Cf. A086797 (n^n + (-1)^n (n-1)^(n-1) with signs). Sequence in context: A167702 A350195 A064687 * A252263 A252361 A252082 Adjacent sequences: A238191 A238192 A238193 * A238195 A238196 A238197 KEYWORD nonn,hard AUTHOR T. D. Noe, Feb 24 2014 EXTENSIONS a(7)-a(44) from Giovanni Resta, Feb 24 2014 STATUS approved

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Last modified June 3 12:17 EDT 2023. Contains 363110 sequences. (Running on oeis4.)