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

1,1

Comments

Numbers k such that A351064(k) = 4.

Links

Table of n, a(n) for n=1..56.

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.

Example

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).

Crossrefs

Cf. A351062, A351066, A351064.

Sequence in context: A374004 A102041 A232488 * A070792 A178893 A340162

Adjacent sequences: A351060 A351061 A351062 * A351064 A351065 A351066

Keyword

nonn

Author

Alberto Zanoni, Feb 22 2022

Extensions

Missing terms inserted by Alberto Zanoni, Jan 08 2024

Status

approved