A395432 Minimum k such that k^9 can be expressed as the sum of n distinct positive 9th powers.

917, 252, 202, 107, 66, 58, 69, 53, 47, 62, 59, 56, 58, 58, 55, 58, 49, 52, 56, 56, 58, 60, 59, 63, 63, 63, 66, 67, 66, 66, 69, 68, 71, 72, 69, 74, 75, 77, 76, 78, 79, 82, 81, 84, 82, 86, 84, 89, 88, 92, 93, 94, 94, 95, 97, 98, 98, 100

Offset

10,1

Comments

No solutions are known for n < 10 according to Eric Weisstein's World of Mathematics.

Links

Zhining Yang, Table of n, a(n) for n = 10..88

Eric Weisstein's World of Mathematics, Diophantine Equation--9th Powers.

Example

a(10) = 917 because 917^9 = 851^9 + 822^9 + 668^9 + 625^9 + 574^9 + 542^9 + 475^9 + 179^9 + 99^9 + 42^9 and no integer smaller than 919 can be expressed as the sum of 10 distinct positive 9th powers.
a(12) = 202 because 202^9 = 187^9 + 169^9 + 165^9 + 162^9 + 89^9 + 64^9 + 62^9 + 57^9 + 53^9 + 18^9 + 15^9 + 1^9 and no integer smaller than 202 can be expressed as the sum of 12 distinct positive 9th powers.

Mathematica

a[n_]:=FirstCase[Range[n+1, 80], k_/; Length[Select[IntegerPartitions[k^9, {n}, Range[k-1]^9], DuplicateFreeQ]]>0]; a[15]

Crossrefs

Cf. A130012, A130022, A018935, A394979, A393280, A395180.

Sequence in context: A234993 A234764 A282592 * A029897 A221387 A217226

Adjacent sequences: A395429 A395430 A395431 * A395434 A395435 A395437

Keyword

nonn

Author

Zhining Yang, Apr 22 2026

Status

approved