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A301601 Numbers k such that k^6 can be written as a sum of 11 positive 6th powers. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A146331 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

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Last modified May 19 07:04 EDT 2019. Contains 323386 sequences. (Running on oeis4.)