A375335 - OEIS

%I #9 Aug 13 2024 07:44:39

%S 1,1,25,23,17

%N a(n) is the smallest positive integer whose square can be represented as the sum of n distinct nonzero squares in exactly n ways, or -1 if no such integer exists.

%C a(6) = 16, a(10) = 25; a(5) > 500, a(7..9) > 100 if not -1  - _Michael S. Branicky_, Aug 13 2024

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e a(2) = 25: 25^2 =  7^2 + 24^2

%e                 = 15^2 + 20^2.

%e .

%e a(3) = 23: 23^2 = 3^2 +  6^2 + 22^2

%e                 = 3^2 + 14^2 + 18^2

%e                 = 6^2 + 13^2 + 18^2.

%e .

%e a(4) = 17: 17^2 = 2^2 + 4^2 + 10^2 + 13^2

%e                 = 2^2 + 5^2 +  8^2 + 14^2

%e                 = 2^2 + 8^2 + 10^2 + 11^2

%e                 = 3^2 + 6^2 + 10^2 + 12^2.

%Y Cf. A006339, A374805, A350241.

%K nonn,more

%O 0,3

%A _Ilya Gutkovskiy_, Aug 12 2024