A128972 n^3 - 1 divided by its largest cube divisor.

7, 26, 63, 124, 215, 342, 511, 91, 37, 1330, 1727, 2196, 2743, 3374, 4095, 614, 17, 254, 7999, 9260, 10647, 12166, 13823, 1953, 17575, 19682, 813, 24388, 26999, 29790, 32767, 4492, 39303, 42874, 46655, 1876, 54871, 59318, 63999, 8615, 74087, 79506

Offset: 2

Author

Jonathan Vos Post, Apr 28 2007

Keywords

• easy
• nonn

Comments

In other words, cubefree part of n^3-1, or cubefree kernel of n^3-1. Cube analog of A068310.

Examples

			a(9) = (9^3-1)/8 = (2^3 * 7 * 13)/(2^3) = 728/8 = 91.
a(10) = (10^3-1)/27 = (3^3 * 37)/(3^3) = 999/27 = 37.
a(18) = (18^3-1)/343 = (7^3 * 17)/(7^3) = 5831/343 = 17.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A002350, A004709, A007948, A062378, A067872, A033314, A068310.

Programs

Maple

a:= n -> mul(f[1]^(f[2] mod 3), f = ifactors(n^3-1)[2]):
seq(a(n),n=2..100); # Robert Israel, Sep 24 2014

Formula

a(n) = A062378(A068601(n)) = A062378(n^3-1).

Extensions

More terms from Carl R. White, Nov 09 2010