A351063 Sums of four perfect powers with different exponents: m = a^x + b^y + c^z + d^t with a > 0, b > 0, c > 0, d > 0, x > 1, y > 1, z > 1, t > 1 and x, y, z, t are all different, with m not representable with fewer such addends.

7, 14, 19, 22, 30, 35, 39, 46, 54, 61, 67, 70, 78, 87, 94, 99, 103, 110, 111, 115, 119, 120, 139, 147, 167, 179, 183, 188, 195, 199, 211, 230, 237, 303, 318, 331, 335, 339, 342, 355, 399, 410, 419, 421, 429, 436, 438, 454, 461, 467, 470, 477, 483, 494, 510, 534

Offset: 1

Author

Alberto Zanoni, Feb 22 2022

Keywords

• nonn

Comments

Numbers k such that A351064(k) = 4.

Examples

			7 is a term, as 7 = 2^2 + 1^3 + 1^4 + 1^5 (considering minimal possible exponents for bases equal to 1).
14 is a term, as 14 = 2^2 + 2^3 + 1^4 + 1^5 (idem).
195 is a term, as 195 = 7^2 + 1^3 + 3^4 + 2^6 or 7^2 + 4^3 + 3^4 + 1^5 or 9^2 + 1^3 + 3^4 + 2^5 (idem).
		

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.
• Alberto Zanoni, Sums of different powers.

Crossrefs

Cf. A351062, A351066, A351064.

Extensions

Missing terms inserted by Alberto Zanoni, Jan 08 2024