A394979 Minimum k such that k^5 can be expressed as the sum of n distinct positive 5th powers.

144, 72, 12, 23, 35, 29, 32, 24, 28, 33, 30, 28, 33, 32, 32, 34, 37, 37, 40, 41, 40, 45, 43, 47, 50, 51, 51, 54, 56, 56, 57, 61, 61, 61, 65, 66, 69, 71, 72, 74, 76, 75, 79, 81, 82, 84, 87, 89, 90, 91, 94, 97, 97, 99, 100, 103, 104, 106, 108, 108, 110, 115, 114

Offset

4,1

Links

Zhining Yang, Table of n, a(n) for n = 4..80

Eric Weisstein's World of Mathematics, Diophantine Equation--5th Powers.

Example

a(4) = 144 because 144^5 = 133^5 + 110^5 + 84^5 + 27^5 and no integer smaller than 144 can be expressed as the sum of 4 distinct positive 5th powers.
a(7) = 23 because 23^5 = 20^5 + 18^5 + 15^5 + 14^5 + 8^5 + 7^5 + 1^5 and no integer smaller than 23 can be expressed as the sum of 7 distinct positive 5th powers.

Mathematica

a[n_]:=FirstCase[Range[n+1, 200], k_/; Length[Select[IntegerPartitions[k^5, {n}, Range[k-1]^5], DuplicateFreeQ]]>0]; Array[a, 10, 4]

Crossrefs

Cf. A000539, A130012, A130022, A018935, A393280.

Sequence in context: A030122 A057404 A173713 * A252485 A185589 A093159

Adjacent sequences: A394976 A394977 A394978 * A394980 A394981 A394982

Keyword

nonn

Author

Zhining Yang, Apr 08 2026

Status

approved