A301601 Numbers k such that k^6 can be written as a sum of 11 positive 6th powers.

18, 19, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93

Offset

1,1

Comments

If k is in the sequence, then k*m is in the sequence for every positive integer m.

Conjecture: 35 is the largest integer not in the sequence. - Jon E. Schoenfield, Mar 24 2018

Links

Table of n, a(n) for n=1..65.

Eric Weisstein's World of Mathematics, Diophantine Equation 6th Powers.

Example

18^6 = 2^6 + 5^6 + 5^6 +  5^6 +  7^6 +  7^6 +  9^6 +  9^6 + 10^6 + 14^6 + 17^6.
19^6 = 1^6 + 7^6 + 7^6 +  7^6 +  8^6 + 12^6 + 13^6 + 13^6 + 13^6 + 13^6 + 17^6.
30^6 = 1^6 + 2^6 + 7^6 +  7^6 +  9^6 + 12^6 + 17^6 + 17^6 + 19^6 + 23^6 + 28^6.
31^6 = 3^6 + 4^6 + 7^6 +  7^6 + 11^6 + 11^6 + 13^6 + 13^6 + 23^6 + 25^6 + 28^6.
32^6 = 7^6 + 7^6 + 7^6 + 17^6 + 17^6 + 17^6 + 18^6 + 20^6 + 20^6 + 25^6 + 29^6.
33^6 = 1^6 + 4^6 + 4^6 +  6^6 + 10^6 + 14^6 + 20^6 + 20^6 + 24^6 + 28^6 + 28^6.
34^6 = 1^6 + 1^6 + 2^6 +  5^6 +  7^6 +  7^6 + 12^6 + 17^6 + 23^6 + 28^6 + 31^6.
36^6 = 1^6 + 1^6 + 1^6 +  7^6 + 14^6 + 14^6 + 19^6 + 19^6 + 19^6 + 30^6 + 33^6.

Crossrefs

Cf. A003294, A297305.

Sequence in context: A308894 A031956 A095393 * A056022 A118510 A022108

Adjacent sequences: A301598 A301599 A301600 * A301602 A301603 A301604

Keyword

nonn

Author

Seiichi Manyama, Mar 24 2018

Extensions

a(9)-a(65) from Jon E. Schoenfield, Mar 24 2018

Status

approved