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A293284 Numbers n such that n^2 = a^2 + b^5 (with integers a, b > 0) and gcd(a, b, n) = 1. 4

%I

%S 9,122,251,257,499,1563,1684,1945,3133,3381,5069,8193,8404,8435,8525,

%T 9966,11317,16815,17063,18751,24999,25001,25243,29525,31087,37928,

%U 41807,59057,59305,62209,65333,67241,79015,80526,80647,82088,84049,88929,110050,134457

%N Numbers n such that n^2 = a^2 + b^5 (with integers a, b > 0) and gcd(a, b, n) = 1.

%C Subsequence of A293283.

%H Chai Wah Wu, <a href="/A293284/b293284.txt">Table of n, a(n) for n = 1..10000</a>

%e 9^2 = 7^2 + 2^5 and gcd(7, 2, 9) = 1.

%e 122^2 = 121^2 + 3^5 and gcd(121, 3, 122) = 1.

%e 88929^2 = 72122^2 + 77^5 and gcd(88929,72122,77) = 1. - _Chai Wah Wu_, Oct 07 2017

%t Do[If[IntegerQ[(n^2 - a^2)^(1/5)] && GCD[a, n] == 1, Print[n]], {n, 134600}, {a, (n^2 - 1)^(1/2)}]

%o (PARI) isok(n) = for (k=1, n-1, if (ispower(n^2-k^2, 5, &m) && (gcd([n, k, m])==1), return (1));); return (0); \\ _Michel Marcus_, Oct 07 2017

%Y Cf. A293283.

%K nonn

%O 1,1

%A _XU Pingya_, Oct 04 2017

%E Term 88929 added by _Chai Wah Wu_, Oct 07 2017

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Last modified September 20 00:58 EDT 2021. Contains 347577 sequences. (Running on oeis4.)