A373970 - OEIS

%I #20 Jun 27 2024 11:31:02

%S 1,9,25,121,784,1024,5041,363609,542939080336,160351569000000,

%T 51312167754301440000,65249379457597440000,449519240612413440000,

%U 957230928468541440000,4797276365676433637376,16367773504928806600704,308090303428827709440000

%N Squares equal to the sum of a cube and a factorial number.

%e 1 = 0^3 + 1!.

%e 25 = 1^3 + 4!.

%e 784 = 4^3 + 6!.

%e 5041 = 1^3 + 7!.

%o (PARI) is1(n) = {my(sq = n^2, f = 1, k = 1); while(f <= sq && !ispower(sq - f, 3), k++; f *= k); f <= sq;}

%o lista(kmax) = for(k = 1, kmax, if(is1(k), print1(k^2, ", "))); \\ _Amiram Eldar_, Jun 24 2024

%Y Cf. A000142, A000290, A000578, A373218.

%Y A085692 is a subsequence.

%K nonn,more

%O 1,2

%A _Martin Ehrenstein_, Jun 24 2024

%E a(10) from _Amiram Eldar_, Jun 24 2024

%E a(11)-a(16) from _David A. Corneth_, Jun 24 2024

%E a(17) from _Michael S. Branicky_, Jun 26 2024