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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.

%I A351062 #31 Aug 16 2025 10:04:25
%S A351062 2,5,10,12,17,20,24,26,28,31,33,37,40,41,43,44,48,50,52,57,59,63,65,
%T A351062 68,72,73,76,80,82,85,89,90,91,96,97,101,106,108,113,116,117,122,126,
%U A351062 127,129,130,132,134,136,137,141,145,148,150,152,153,155,157,160,161,162,164,170
%N 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.
%H A351062 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 A351062 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.
%e A351062 2 is a term, as 2 = 1^2 + 1^3.
%e A351062 5 is a term, as 5 = 2^2 + 1^3.
%e A351062 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).
%Y A351062 Cf. A001597, A070049, A327609.
%K A351062 nonn
%O A351062 1,1
%A A351062 _Alberto Zanoni_, Jan 31 2022
%E A351062 Definition clarified by _Alberto Zanoni_, Feb 28 2022