A104492 Cube excess of the n-th prime.

1, 2, 4, 6, 3, 5, 9, 11, 15, 2, 4, 10, 14, 16, 20, 26, 32, 34, 3, 7, 9, 15, 19, 25, 33, 37, 39, 43, 45, 49, 2, 6, 12, 14, 24, 26, 32, 38, 42, 48, 54, 56, 66, 68, 72, 74, 86, 7, 11, 13, 17, 23, 25, 35, 41, 47, 53, 55, 61, 65, 67, 77, 91, 95, 97, 101, 115, 121, 4, 6, 10, 16, 24, 30

Offset: 1

Author

Jonathan Vos Post, Mar 10 2005

Keywords

• easy
• nonn

Examples

			a(48) = 7 because the 48th prime is 223 and 223 - 6^3 = 7, while 223 - 7^3 = -120.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A053186, A055400, A056892, A102821.

Programs

Mathematica

lst={};Do[p=Prime[n];s=p^(1/3);f=Floor[s];a=f^3;d=p-a;AppendTo[lst,d],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
#-Floor[Surd[#,3]]^3&/@Prime[Range[80]] (* Harvey P. Dale, Feb 15 2018 *)

Formula

a(n) = A055400(A000040(n)).

a(n) = prime(n) - floor(prime(n)^(1/3))^3. - Jon E. Schoenfield, Jan 17 2015