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A078380 Maximum exponent in prime factorization of numbers which can be written as sum of a positive square and a positive cube.

%I A078380 #9 Mar 27 2025 04:23:40
%S A078380 1,1,2,1,2,1,3,1,2,1,1,2,1,1,2,2,2,1,2,1,2,3,1,2,4,1,1,1,2,1,3,1,1,2,
%T A078380 1,7,1,1,1,1,2,2,3,1,2,1,2,1,1,1,3,2,1,2,1,4,1,2,1,2,1,3,1,1,1,2,1,2,
%U A078380 3,1,1,3,1,2,1,2,3,2,6,1,2,2,1,3,1,2,3,5,1,1,3,1,4,2,1,1,1,2,3,1,1,3,2,2,3
%N A078380 Maximum exponent in prime factorization of numbers which can be written as sum of a positive square and a positive cube.
%H A078380 Amiram Eldar, <a href="/A078380/b078380.txt">Table of n, a(n) for n = 1..10000</a>
%F A078380 a(n) = A051903(A055394(n)).
%t A078380 Max[FactorInteger[#][[;; , 2]]] & /@ Select[Range[300], Length[Reduce[a^2 + b^3 == # && a > 0 && b > 0, {a, b}, Integers]] > 0 &] (* _Amiram Eldar_, Mar 27 2025 *)
%Y A078380 Cf. A051903, A055394, A078377, A078379.
%K A078380 nonn
%O A078380 1,3
%A A078380 _Reinhard Zumkeller_, Nov 25 2002