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a(n) is the least positive integer that can be expressed as the sum of one or more consecutive perfect powers (A001597) in exactly n ways, or -1 if no such integer exists.
1

%I #12 May 19 2023 14:18:55

%S 1,25,441

%N a(n) is the least positive integer that can be expressed as the sum of one or more consecutive perfect powers (A001597) in exactly n ways, or -1 if no such integer exists.

%C a(4) > 1.5 * 10^8.

%C No further terms < 2.8*10^14. - _Michael S. Branicky_, Apr 20 2023

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>

%e For n = 2: 25 = 25 = 9 + 16.

%e For n = 3: 441 = 441 = 216 + 225 = 128 + 144 + 169.

%Y Cf. A001597.

%K nonn,bref,more

%O 1,2

%A _Ilya Gutkovskiy_, Apr 19 2023