A226973 Difference between n! and the largest cube < n!.

1, 1, 5, 16, 56, 208, 127, 1016, 4969, 47223, 264979, 789832, 7668081, 4272696, 130217625, 883909125, 9969785792, 52152119144, 128092980744, 2166664965184, 29992267884032, 272465658461528, 1588888484126208, 10747891377020979, 5480400487212279, 70703132766750784, 1908984584702271168

Offset: 1

Author

Zak Seidov, Jun 25 2013

Keywords

• nonn

Comments

Also, smallest number k such that n! - k is a cube.

Sequence is not monotonic: a(n) < a(n-1) for n: 7, 14, 25, 30, 51, 106, 168, 279, 288.

Examples

			a(2) = 2! - 1^3 = 1, a(3) = 3! - 1^3 = 5, a(4) = 4! - 3^3 = 16.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000142, A066857, A214083.

Programs

Mathematica

Join[{1}, Table[n! - Floor[(n!)^(1/3)]^3, {n, 2, 30}]]

PARI

a(n)=my(N=n!);N-sqrtnint(N,3)^3 \\ Charles R Greathouse IV, Jun 25 2013

Formula

a(n) = n! - floor (n!^(1/3))^3 = A000142(n) - A214083(n)^3.