A368161 a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.

1, 25, 441, 100, 169, 289, 121, 2395417249

Offset: 1

Author

J. Stauduhar and Tim Peters, Dec 14 2023

Keywords

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Comments

It is conjectured that m always exists.

The present state of knowledge (with ? for unknown entries) is:

1, 25, 441, 100, 169, 289, 121, 2395417249, ?, 15386237159377984, 676, 232324, ?, ?, ?, 64866916, 3721, 3622354596, 279936, ?, ?, 41152225, 29929, 2137444, ?, 11526025, 97969, 9922500, ?, 978626089, ?, 347151424, ?

Known solutions < 10^12 from J. Stauduhar. All others from Tim Peters.

Examples

			128 + 144 + 169 = 441, and 441 is the first perfect power that is the sum of three consecutive perfect powers, so a(3) = 441.
		

Links

• J. Stauduhar, 3772 known solutions.

Crossrefs

Cf. A001597.