

A238194


Conjectured numbers n for which n^n + (1)^n (n1)^(n1) 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
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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 (n1)^(n1) 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.
Giovanni Resta, Terms < 200000 and corresponding square divisors


PROG

(PARI) is(n)=!issquarefree(n^n + (1)^n*(n1)^(n1)) \\ Charles R Greathouse IV, Feb 25 2014


CROSSREFS

Cf. A086797 (n^n + (1)^n (n1)^(n1) 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



