%I #30 Nov 24 2024 14:00:59
%S 0,1,2,3,4,6,8,10,14,16,17,19,20,21,22,23,24,25
%N Integers n such that n! = x^2 + y^3 + z^6 where x, y and z are nonnegative integers, is soluble.
%C Conjecture I: Natural density of this sequence is 1.
%C Conjecture II: Any sufficiently large n is in the sequence.
%C Conjecture III: There is a fixed value of t such that all integers >= t are terms.
%C If k is of the form x^2 + y^3 + z^6 then so is k*m^6 = (x*m^3)^2 + (y*m^2)^3 + (z*m)^6. - _David A. Corneth_, Aug 13 2020
%H David A. Corneth, <a href="/A337046/a337046.gp.txt">PARI program</a>
%e 6 is a term since 6! = 12^2 + 8^3 + 2^6.
%o (PARI) \\ See Corneth link. _David A. Corneth_, Aug 13 2020
%Y Cf. A267414, A273553 (subsequence).
%K nonn,more
%O 1,3
%A _Altug Alkan_, Aug 12 2020
%E a(12)-a(18) from _David A. Corneth_, Aug 12 2020