cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-13 of 13 results.

A295976 Number of nonnegative solutions to (x,y) = 1 and x^3 + y^3 = n.

Original entry on oeis.org

0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
Offset: 0

Views

Author

Seiichi Manyama, Dec 01 2017

Keywords

Comments

Number of ordered pairs of two nonnegative natural numbers that are coprime and whose cubes add to n. - Antti Karttunen, May 31 2021

Examples

			For 1729, a(1729) = 4, because the following four ordered pairs, (1,12),  (9,10),  (10,9) and (12,1) satisfy the condition, as 1^3 + 12^3 = 9^3 + 10^3 = 1729. - _Antti Karttunen_, May 31 2021

Links

Crossrefs

Cf. A173677, A225530, A295819, A295977.
Cf. also A202679.

Programs

  • PARI
    {a(n) = sum(i=0, n, sum(j=0, n, if((gcd(i, j)==1) && (i^3+j^3==n), 1, 0)))}
  • PARI
    A295976(n) = { my(s=0); for(i=0, oo, i3 = i^3; forstep(j=n-i3, 0, -1, if((i3+j^3==n) && gcd(i, j)==1, s++)); if(i3>n, return(s))); }; \\ Antti Karttunen, May 31 2021

A069136 Numbers that are not the sum of 5 nonnegative cubes.

Original entry on oeis.org

6, 7, 13, 14, 15, 20, 21, 22, 23, 34, 39, 41, 42, 46, 47, 48, 49, 50, 53, 58, 60, 61, 69, 76, 77, 79, 84, 85, 86, 87, 95, 98, 102, 103, 104, 105, 106, 110, 111, 112, 113, 114, 117, 121, 122, 123, 124, 132, 139, 140, 147, 148, 151, 158, 159, 165
Offset: 1

Views

Author

N. J. A. Sloane, Apr 08 2002

Keywords

Comments

Sequence is conjectured to be finite.
Comment from Richard C. Schroeppel, Sep 22 2010: It is conjectured that 7373170279850 is the largest number requiring more than four cubes (see Deshouillers et al.).

References

  • Bohman, Jan and Froberg, Carl-Erik; Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
  • F. Romani, Computations concerning Waring's problem, Calcolo, 19 (1982), 415-431.

Links

Crossrefs

Sums of k cubes, number of ways of writing n as, for k=1..9: A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

A363776 Expansion of 1/(Sum_{k>=0} x^(k^3))^2.

Original entry on oeis.org

1, -2, 3, -4, 5, -6, 7, -8, 7, -4, -1, 8, -17, 28, -41, 56, -70, 80, -83, 76, -56, 20, 35, -112, 210, -324, 445, -562, 658, -712, 699, -590, 357, 22, -558, 1252, -2084, 3008, -3947, 4788, -5383, 5556, -5116, 3864, -1618, -1756, 6307, -11956, 18454, -25348, 31962, -37380
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2023

Keywords

Crossrefs

Convolution inverse of A173677.
Column k=2 of A363779.
Cf. A363783.

Programs

  • PARI
    my(N=60, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/3), x^k^3)^2)

Formula

a(0) = 1; a(n) = -(2/n) * Sum_{k=1..n} A363783(k) * a(n-k).
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.