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

Author

Seiichi Manyama, Mar 24 2018

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A003294, A297305.

Extensions

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