A181354 Number of n-digit perfect cubes.

2, 2, 5, 12, 25, 53, 116, 249, 535, 1155, 2487, 5358, 11545, 24871, 53584, 115444, 248715, 535841, 1154435, 2487154, 5358411, 11544347, 24871542, 53584111, 115443470, 248715414, 535841116, 1154434691, 2487154143, 5358411166

Offset: 1

Author

Martin Renner, Jan 28 2011

Keywords

• nonn
• base

Comments

a(n) is also the total number of n-digit numbers requiring 1 positive cube in their representation as sum of cubes.

a(n) + A181376(n) + A181378(n) + A181380(n) + A181384(n) + A181401(n) + A181403(n) + A181405(n) + A171386(n) = A052268(n).

Differs from A062941 only at n=1, because 0 is considered a 0-digit, not a 1-digit number here. - R. J. Mathar, Jul 09 2011

Links

• Eric Weisstein's World of Mathematics, Waring's Problem.

Crossrefs

Cf. A000578

Programs

Maple

a:=n->ceil(10^(n/3))-ceil(10^((n-1)/3));

Mathematica

With[{c = Range[4650000]^3}, Length[#]&/@Table[Select[c, IntegerLength[#] == n &], {n, 20}]] (* Harvey P. Dale, Feb 01 2011 *)
Differences[Ceiling[10^(Range[0, 30]/3)]]

Formula

a(n) = A061439(n) - A061439(n-1).

Extensions

More terms from T. D. Noe, Feb 01 2011