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A301601 Numbers k such that k^6 can be written as a sum of 11 positive 6th powers. 1

%I

%S 18,19,30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,

%T 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,

%U 75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93

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

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

%C Conjecture: 35 is the largest integer not in the sequence. - _Jon E. Schoenfield_, Mar 24 2018

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiophantineEquation6thPowers.html">Diophantine Equation 6th Powers.</a>

%e 18^6 = 2^6 + 5^6 + 5^6 + 5^6 + 7^6 + 7^6 + 9^6 + 9^6 + 10^6 + 14^6 + 17^6.

%e 19^6 = 1^6 + 7^6 + 7^6 + 7^6 + 8^6 + 12^6 + 13^6 + 13^6 + 13^6 + 13^6 + 17^6.

%e 30^6 = 1^6 + 2^6 + 7^6 + 7^6 + 9^6 + 12^6 + 17^6 + 17^6 + 19^6 + 23^6 + 28^6.

%e 31^6 = 3^6 + 4^6 + 7^6 + 7^6 + 11^6 + 11^6 + 13^6 + 13^6 + 23^6 + 25^6 + 28^6.

%e 32^6 = 7^6 + 7^6 + 7^6 + 17^6 + 17^6 + 17^6 + 18^6 + 20^6 + 20^6 + 25^6 + 29^6.

%e 33^6 = 1^6 + 4^6 + 4^6 + 6^6 + 10^6 + 14^6 + 20^6 + 20^6 + 24^6 + 28^6 + 28^6.

%e 34^6 = 1^6 + 1^6 + 2^6 + 5^6 + 7^6 + 7^6 + 12^6 + 17^6 + 23^6 + 28^6 + 31^6.

%e 36^6 = 1^6 + 1^6 + 1^6 + 7^6 + 14^6 + 14^6 + 19^6 + 19^6 + 19^6 + 30^6 + 33^6.

%Y Cf. A003294, A297305.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Mar 24 2018

%E a(9)-a(65) from _Jon E. Schoenfield_, Mar 24 2018

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Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)