A354761 Least number of squares and cubes that add up to n.

1, 2, 3, 1, 2, 3, 4, 1, 1, 2, 3, 2, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 1, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 1, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 1, 2, 3, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 1, 2, 3, 3, 2, 3

Offset

1,2

Comments

a(n) <= 4 since any number can be written as a sum of 4 squares (Lagrange's theorem).

Sequence first differs from A063274, A225926 and A274459 at n = 32 since 32 is a powerful number, a prime power and a perfect power but neither a square nor a cube.

Links

Table of n, a(n) for n=1..86.

Example

a(1) = 1, a(4) = 1 (4 = 2^2), a(7) = 4 (7 = 2^2 + 1^2 + 1^2 + 1^2), a(8) = 1 (8 = 2^3), a(12) = 2 (12 = 2^3 + 2^2), a(17) = 2 (17 = 4^2 + 1^2), a(32) = 2 (32 = 4^2 + 4^2).

Prog

(PARI) lista(n) = {my(v = vector(n)); for(j = 2, 3, for(i = 2, sqrtnint(n, j), v[i^j] = 1)); v[1]=1; v[2]=2; for(i=3, #v, if(v[i]==0, v[i] = vecmin(vector(i\2, k, v[k] + v[i-k])))); v}

Crossrefs

Cf. A002760, A063274, A225926, A274459, A002376, A002828, A000290, A000578.

Sequence in context: A063274 A274459 A225926 * A351064 A339822 A194063

Adjacent sequences: A354758 A354759 A354760 * A354762 A354763 A354764

Keyword

nonn

Author

Peter Schorn, Jun 06 2022

Status

approved