A395180 Minimum k such that k^7 can be expressed as the sum of n distinct positive 7th powers.

568, 102, 62, 89, 54, 57, 49, 47, 40, 45, 43, 43, 44, 46, 45, 44, 47, 46, 48, 49, 47, 47, 52, 55, 52, 57, 57, 57, 60, 61, 61, 64, 65, 65, 69, 69, 70, 69, 72, 75, 77, 77, 78, 78, 82, 84, 86, 83, 87, 89, 90, 93, 93, 95, 94, 97, 98, 101, 100, 104, 104, 106, 108, 110

Offset

7,1

Links

Zhining Yang, Table of n, a(n) for n = 7..100

Eric Weisstein's World of Mathematics, Diophantine Equation--7th Powers.

Example

a(7) = 568 because 568^7 = 525^7 + 439^7 + 430^7 + 413^7 + 266^7 + 258^7 + 127^7 and no integer smaller than 568 can be expressed as the sum of 7 distinct positive 7th powers.
a(9) = 62 because 62^7 = 59^7 + 50^7 + 41^7 + 33^7 + 27^7 + 22^7 + 20^7 + 14^7 + 6^7 and no integer smaller than 62 can be expressed as the sum of 9 distinct positive 7th powers.

Mathematica

a[n_]:=FirstCase[Range[n+1, 70], k_/; Length[Select[IntegerPartitions[k^7, {n}, Range[k-1]^7], DuplicateFreeQ]]>0]; a[12]

Crossrefs

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

Sequence in context: A209954 A233057 A087424 * A381026 A134922 A322688

Adjacent sequences: A395177 A395178 A395179 * A395181 A395182 A395183

Keyword

nonn

Author

Zhining Yang, Apr 15 2026

Status

approved