A373218 - OEIS

%I #22 Jun 24 2024 04:41:52

%S 1,27,729,46656

%N Cubes equal to the sum of a factorial number and a square.

%C Cubes c^3 for which the c-th row of A167222 includes a factorial number. - _Michel Marcus_, May 28 2024

%C a(5) > 8*10^24. - _Michael S. Branicky_, Jun 23 2024

%C a(5) > 10^38. - _Martin Ehrenstein_, Jun 24 2024

%e 1 = 1! + 0^2.

%e 27 = 2! + 5^2.

%e 729 = 6! + 3^2.

%e 46656 = 7! + 204^2.

%o (PARI) isok(k) = my(c=k^3, i=1, p=1); while (1, if (issquare(c-p), return(1)); i++; p *=i; if (p> c, return(0)););

%o for (n=1, 50, if (isok(n), print1(n^3, ", "))); \\ _Michel Marcus_, Jun 06 2024

%Y Cf. A000142, A000290, A000578, A167222.

%K nonn,more

%O 1,2

%A _Gonzalo Martínez_, May 28 2024