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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.
4

%I #25 Mar 01 2022 07:26:47

%S 2,5,10,12,17,20,24,26,28,31,33,37,40,41,43,44,48,50,52,57,59,63,65,

%T 68,72,73,76,80,82,85,89,90,91,96,97,101,106,108,113,116,117,122,126,

%U 127,129,130,132,134,136,137,141,145,148,150,152,153,155,157,160,161,162,164,170

%N 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.

%e 2 is a term, as 2 = 1^2 + 1^3.

%e 5 is a term, as 5 = 2^2 + 1^3.

%e 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 Cf. A001597, A070049, A327609.

%K nonn

%O 1,1

%A _Alberto Zanoni_, Jan 31 2022

%E Definition clarified by _Alberto Zanoni_, Feb 28 2022