A373218 Cubes equal to the sum of a factorial number and a square.

1, 27, 729, 46656

Offset: 1

Author

Gonzalo Martínez, May 28 2024

Keywords

• nonn
• more

Comments

Cubes c^3 for which the c-th row of A167222 includes a factorial number. - Michel Marcus, May 28 2024

a(5) > 8*10^24. - Michael S. Branicky, Jun 23 2024

a(5) > 10^38. - Martin Ehrenstein, Jun 24 2024

Examples

			1 = 1! + 0^2.
27 = 2! + 5^2.
729 = 6! + 3^2.
46656 = 7! + 204^2.
		

Crossrefs

Cf. A000142, A000290, A000578, A167222.

Programs

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)););
for (n=1, 50, if (isok(n), print1(n^3, ", "))); \\ Michel Marcus, Jun 06 2024