A393280 Minimum k such that k^6 can be expressed as the sum of n distinct positive 6th powers.

1141, 251, 123, 54, 53, 46, 43, 42, 35, 25, 32, 37, 41, 48, 49, 49, 49, 48, 45, 47, 48, 52, 55, 55, 53, 50, 55, 59, 57, 65, 67, 63, 66, 65, 68, 67, 71, 73, 77, 79, 79, 81, 81, 81, 83, 85, 89, 90, 90, 93, 94, 94, 96, 100, 104, 104, 104, 105, 103, 105, 108, 111

Offset

7,1

Links

Zhao Hui Du, Table of n, a(n) for n = 7..199 (terms 7..87 from Zhining Yang)

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

Example

a(7) = 1141 because 1141^6 = 1077^6 + 894^6 + 702^6 + 474^6 + 402^6 + 234^6 + 74^6 and no integer smaller than 1141 can be expressed as the sum of 7 distinct positive 6th powers.
a(9) = 123 because 123^6 = 112^6 + 106^6 + 62^6 + 46^6 + 40^6 + 22^6 + 8^6 + 5^6 + 4^6 and no integer smaller than 123 can be expressed as the sum of 9 distinct positive 6th powers.

Mathematica

a[n_]:=FirstCase[Range[n+1, 60], k_/; Length[Select[IntegerPartitions[k^6, {n}, Range[k-1]^6], DuplicateFreeQ]]>0]; a[12]

Crossrefs

Cf. A130012, A130022, A018935, A252476, A252486, A261572, A394979.

Sequence in context: A232133 A261572 A252476 * A020397 A132410 A252428

Adjacent sequences: A393277 A393278 A393279 * A393281 A393282 A393283

Keyword

nonn

Author

Zhining Yang, Apr 08 2026

Extensions

a(49) and a(61) corrected by Zhao Hui Du, Apr 16 2026

Status

approved