A394897 a(n) is the smallest number k such that k^n is the sum of 3n distinct positive n-th powers.

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

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Example

6^1 = 3^1+2^1+1^1;
13^2 = 9^2+7^2+5^2+3^2+2^2+1^2;
18^3 = 14^3+11^3+10^3+7^3+6^3+5^3+4^3+2^3+1^3;
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;
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;
...

Mathematica

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

Crossrefs

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

Sequence in context: A032366 A287237 A282975 * A094696 A095911 A013575

Adjacent sequences: A394894 A394895 A394896 * A394898 A394899 A394900

Keyword

nonn,more,hard

Author

Zhining Yang, May 20 2026

Status

approved