A383122 a(n) is the smallest number that can be expressed as the sum of the smallest number of powers with different exponents greater than one in n different ways (for unitary bases, the smallest possible exponents are considered).

1, 16, 17, 65, 80, 105, 139, 193, 329, 313, 336, 410, 477, 273, 553, 461, 436, 1219, 942, 10153, 1595, 1038, 722, 636, 1769, 1344, 2045, 2381, 1805, 2379, 3683, 2365, 1611, 3319, 3815, 4416, 4838, 4029, 3531, 5606, 5789, 4411, 4341, 5849, 7392, 1642, 4885, 8246, 3074, 5251, 5774, 3165, 2498, 12347, 9987, 5405, 8075, 11101, 2346, 6749

Offset: 1

Author

Alberto Zanoni, Apr 17 2025

Keywords

• nonn

Comments

The sequence is infinite.

Examples

			For n = 1 the sum (1 addend) is 1^2
For n = 2 the sums (1 addend) are 4^2, 2^4
For n = 3 the sums are (2 addends) 1^2 + 2^4, 3^2 + 2^3, 4^2 + 1^3
For n = 4 the sums are (2 addends) 1^2 + 2^6, 1^2 + 4^3, 7^2 + 2^4, 8^2 + 1^3
For n = 5 the sums are (2 addends) 2^4 + 2^6, 4^3 + 2^4, 4^2 + 2^6, 4^2 + 4^3, 8^2 + 2^4
For n = 6 the sums are (3 addends) 3^2 + 2^5 + 2^6, 3^2 + 4^3 + 2^5, 4^2 + 2^3 + 3^4, 5^2 + 2^4 + 2^6, 5^2 + 4^3 + 2^4, 9^2 + 2^3 + 2^4
		

Links

• Eugenio Garista and Alberto Zanoni, Somme di potenze con esponenti diversi, MatematicaMente, 317 (2024), 1-2.
• Eugenio Garista and Alberto Zanoni, Sums of Positive Integer Powers with Unlike Exponents, Armenian Journal of Mathematics, 17 No. 3 (2025), 1-11.
• Alberto Zanoni, Sum of unlike powers for integers

Crossrefs

Cf. A351062, A351066, A351063, A351065, A351064.