cp's OEIS Frontend

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.

%I A351063 #36 Aug 16 2025 10:04:15
%S A351063 7,14,19,22,30,35,39,46,54,61,67,70,78,87,94,99,103,110,111,115,119,
%T A351063 120,139,147,167,179,183,188,195,199,211,230,237,303,318,331,335,339,
%U A351063 342,355,399,410,419,421,429,436,438,454,461,467,470,477,483,494,510,534
%N 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.
%C A351063 Numbers k such that A351064(k) = 4.
%H A351063 E. Garista and A. Zanoni, <a href="https://www.mathesis.verona.it/wp-content/uploads/2018/Numeri/Nume317.pdf">Somme di potenze con esponenti diversi</a>, MatematicaMente, 317 (2024), 1-2.
%H A351063 E. Garista and A. Zanoni, <a href="https://doi.org/10.52737/18291163-2025.17.3-1-11">Sums of positive integer powers with unlike exponents</a>, Armenian Journal of Mathematics, 17 No. 3 (2025), 1-11.
%H A351063 Alberto Zanoni, <a href="https://sum-of-unlike-powers.jimdosite.com/">Sums of different powers</a>.
%e A351063 7 is a term, as 7 = 2^2 + 1^3 + 1^4 + 1^5 (considering minimal possible exponents for bases equal to 1).
%e A351063 14 is a term, as 14 = 2^2 + 2^3 + 1^4 + 1^5 (idem).
%e A351063 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).
%Y A351063 Cf. A351062, A351066, A351064.
%K A351063 nonn
%O A351063 1,1
%A A351063 _Alberto Zanoni_, Feb 22 2022
%E A351063 Missing terms inserted by _Alberto Zanoni_, Jan 08 2024