cp's OEIS Frontend

A238194 Conjectured numbers n for which n^n + (-1)^n (n-1)^(n-1) is not squarefree.

%I A238194 #25 Feb 27 2023 03:22:50
%S A238194 130,257,487,528,815,897,1176,1225,1320,1373,1430,2029,2050,2084,2198,
%T A238194 2247,2526,2608,2895,2936,2958,3166,3679,3849,3909,3950,4237,4319,
%U A238194 4598,4647,4723,4795,5472,5487,5620,5669,5948,6030,6317,6358,6588,6677,6936,7101
%N A238194 Conjectured numbers n for which n^n + (-1)^n (n-1)^(n-1) is not squarefree.
%C A238194 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.
%C A238194 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
%C A238194 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
%H A238194 David W. Boyd, Greg Martin, and Mark Thom, <a href="http://arxiv.org/abs/1402.5148">Squarefree values of trinomial discriminants</a>, arXiv 1402.5148 [math.NT], 2014.
%H A238194 Chandrashekhar Khare, Alfio Fabio La Rosa, and Gabor Wiese, <a href="https://orbilu.uni.lu/bitstream/10993/51645/1/OnSerreJordan-6.pdf"> Splitting fields of X^n - X - 1 (particularly for n = 5), prime decomposition and modular forms</a>, Univ. du Luxembourg (2022).
%H A238194 Giovanni Resta, <a href="/A238194/a238194.txt">Terms < 200000 and corresponding square divisors</a>
%o A238194 (PARI) is(n)=!issquarefree(n^n + (-1)^n*(n-1)^(n-1)) \\ _Charles R Greathouse IV_, Feb 25 2014
%Y A238194 Cf. A086797 (n^n + (-1)^n (n-1)^(n-1) with signs).
%K A238194 nonn,hard
%O A238194 1,1
%A A238194 _T. D. Noe_, Feb 24 2014
%E A238194 a(7)-a(44) from _Giovanni Resta_, Feb 24 2014