A394897 - OEIS

%I #41 Jun 01 2026 22:43:37

%S 6,13,18,43,28,37,45,99,52,81,78

%N a(n) is the smallest number k such that k^n is the sum of 3n distinct positive n-th powers.

%e 6^1 = 3^1+2^1+1^1;

%e 13^2 = 9^2+7^2+5^2+3^2+2^2+1^2;

%e 18^3 = 14^3+11^3+10^3+7^3+6^3+5^3+4^3+2^3+1^3;

%e 43^4 = 34^4+32^4+26^4+24^4+18^4+16^4+14^4+12^4+10^4+8^4+6^4+3^4;

%e 28^5 = 23^5+20^5+19^5+18^5+17^5+16^5+13^5+12^5+9^5+8^5+7^5+6^5+5^5+3^5+2^5;

%e ...

%t a[n_] := FirstCase[Range[n, 50], k_ /; Length[Select[IntegerPartitions[k^n, {3 n}, Range[k - 1]^n], DuplicateFreeQ]] > 0]; Array[a, 7]

%Y Cf. A000217, A018935, A130012, A130022, A394979, A393280, A395180, A394259, A395432, A007666, A395519.

%K nonn,more,hard

%O 1,1

%A _Zhining Yang_, May 20 2026