A351062 Numbers which are the sum of two perfect powers with different exponents: m = a^x + b^y with a > 0, b > 0, x > 1, y > 1 and x different from y, with m not a perfect power.
2, 5, 10, 12, 17, 20, 24, 26, 28, 31, 33, 37, 40, 41, 43, 44, 48, 50, 52, 57, 59, 63, 65, 68, 72, 73, 76, 80, 82, 85, 89, 90, 91, 96, 97, 101, 106, 108, 113, 116, 117, 122, 126, 127, 129, 130, 132, 134, 136, 137, 141, 145, 148, 150, 152, 153, 155, 157, 160, 161, 162, 164, 170
Offset: 1
Keywords
Examples
2 is a term, as 2 = 1^2 + 1^3. 5 is a term, as 5 = 2^2 + 1^3. 17 is a term, as 17 = 1^2 + 2^4 or 3^2 + 2^3 or 4^2 + 1^3 (considering minimal possible exponents for bases equal to 1).
Links
- E. Garista and A. Zanoni, Somme di potenze con esponenti diversi, MatematicaMente, 317 (2024), 1-2.
- E. Garista and A. Zanoni, Sums of positive integer powers with unlike exponents, Armenian Journal of Mathematics, 17 No. 3 (2025), 1-11.
Extensions
Definition clarified by Alberto Zanoni, Feb 28 2022