A373970 Squares equal to the sum of a cube and a factorial number.

1, 9, 25, 121, 784, 1024, 5041, 363609, 542939080336, 160351569000000, 51312167754301440000, 65249379457597440000, 449519240612413440000, 957230928468541440000, 4797276365676433637376, 16367773504928806600704, 308090303428827709440000

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

1 = 0^3 + 1!.
25 = 1^3 + 4!.
784 = 4^3 + 6!.
5041 = 1^3 + 7!.

Prog

(PARI) is1(n) = {my(sq = n^2, f = 1, k = 1); while(f <= sq && !ispower(sq - f, 3), k++; f *= k); f <= sq; }
lista(kmax) = for(k = 1, kmax, if(is1(k), print1(k^2, ", "))); \\ Amiram Eldar, Jun 24 2024

Crossrefs

Cf. A000142, A000290, A000578, A373218.

A085692 is a subsequence.

Sequence in context: A092769 A263951 A139818 * A227078 A146365 A146373

Adjacent sequences: A373967 A373968 A373969 * A373971 A373972 A373973

Keyword

nonn,more

Author

Martin Ehrenstein, Jun 24 2024

Extensions

a(10) from Amiram Eldar, Jun 24 2024

a(11)-a(16) from David A. Corneth, Jun 24 2024

a(17) from Michael S. Branicky, Jun 26 2024

Status

approved