A396267 a(n) is the smallest number k such that k^n is the sum of 4n distinct positive n-th powers.

10, 17, 22, 53, 37, 48, 47, 109, 66, 74, 78

Offset

1,1

Links

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

Example

10^1 = 4^1+3^1+2^1+1^1;
17^2 = 11^2+8^2+7^2+5^2+4^2+3^2+2^2+1^2;
22^3 = 16^3+13^3+12^3+11^3+8^3+7^3+6^3+5^3+4^3+3^3+2^3+1^3;
53^4 = 40^4+36^4+34^4+32^4+30^4+20^4+18^4+16^4+15^4+14^4+12^4+10^4+8^4+6^4+4^4+2^4;
37^5 = 30^5+28^5+27^5+25^5+17^5+15^5+14^5+13^5+12^5+11^5+10^5+9^5+8^5+7^5+6^5+5^5+4^5+3^5+2^5+1^5;
...

Mathematica

a[n_] := FirstCase[Range[n, 60], k_ /; Length[Select[IntegerPartitions[k^n, {4 n}, Range[k - 1]^n], DuplicateFreeQ]] > 0]; Array[a, 7]

Crossrefs

Cf. A000217, A018935, A130012, A130022, A394979, A393280, A395180, A394259, A395432, A007666, A395519, A394897.

Sequence in context: A280591 A308691 A332226 * A338590 A003333 A345803

Adjacent sequences: A396264 A396265 A396266 * A396268 A396269 A396270

Keyword

nonn,more

Author

Zhining Yang, May 20 2026

Status

approved