A394979 - OEIS

%I #22 Apr 16 2026 00:29:53

%S 144,72,12,23,35,29,32,24,28,33,30,28,33,32,32,34,37,37,40,41,40,45,

%T 43,47,50,51,51,54,56,56,57,61,61,61,65,66,69,71,72,74,76,75,79,81,82,

%U 84,87,89,90,91,94,97,97,99,100,103,104,106,108,108,110,115,114

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

%H Zhining Yang, <a href="/A394979/b394979.txt">Table of n, a(n) for n = 4..80</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantineEquation5thPowers.html">Diophantine Equation--5th Powers</a>.

%e 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.

%e 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.

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

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

%K nonn

%O 4,1

%A _Zhining Yang_, Apr 08 2026