A365041 Primitive solutions of A365008.

12, 30, 32, 67, 78, 99, 106, 112, 113, 119, 135, 139, 145, 147, 156, 161, 172, 178, 189, 190, 197, 202, 205, 210, 214, 222, 223, 225, 227, 228, 234, 235, 236, 237, 241, 242, 243, 249, 251, 252, 257, 258, 260, 268, 272, 273, 277, 278, 280, 286, 287, 294, 295

Offset

1,1

Comments

Numbers k such that k^5 = Sum_{i=1..6} y_i^5 with y_i > 0 and gcd(k,y_1,...,y_6) = 1.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..93

L. J. Lander and T. R. Parkin, A Counterexample to Euler's Sum of Powers Conjecture, Math. Comput. 21, 101-103, 1967.

Index to sequences related to Diophantine equations (5,1,6).

Example

112 is a term since 112^5 = 10^5 + 21^5 + 33^5 + 77^5 + 77^5 + 104^5 and gcd(112, 10, 21, 33, 77, 77, 104) = 1.
268 is a term since 268^5 = 74^5 + 113^5 + 148^5 + 177^5 + 215^5 + 231^5 and gcd(268, 74, 113, 148, 177, 215, 231) = 1.

Crossrefs

Cf. A365008.

Sequence in context: A331367 A335149 A050689 * A144565 A334587 A329947

Adjacent sequences: A365038 A365039 A365040 * A365042 A365043 A365044

Keyword

nonn

Author

Chai Wah Wu, Aug 18 2023

Status

approved