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

1,2

Comments

The sequence is infinite.

Links

Table of n, a(n) for n=1..60.

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

Example

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

Crossrefs

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

Sequence in context: A041522 A097221 A097220 * A041530 A041528 A112012

Adjacent sequences: A383119 A383120 A383121 * A383123 A383124 A383125

Keyword

nonn

Author

Alberto Zanoni, Apr 17 2025

Status

approved