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

9, 122, 251, 257, 499, 1563, 1684, 1945, 3133, 3381, 5069, 8193, 8404, 8435, 8525, 9966, 11317, 16815, 17063, 18751, 24999, 25001, 25243, 29525, 31087, 37928, 41807, 59057, 59305, 62209, 65333, 67241, 79015, 80526, 80647, 82088, 84049, 88929, 110050, 134457

Offset: 1

Author

XU Pingya, Oct 04 2017

Keywords

• nonn

Comments

Subsequence of A293283.

Examples

			9^2 = 7^2 + 2^5 and gcd(7, 2, 9) = 1.
122^2 = 121^2 + 3^5 and gcd(121, 3, 122) = 1.
88929^2 = 72122^2 + 77^5 and gcd(88929,72122,77) = 1. - _Chai Wah Wu_, Oct 07 2017
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A293283.

Programs

Mathematica

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

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

Extensions

Term 88929 added by Chai Wah Wu, Oct 07 2017