A333821 Numbers k that can be represented in the form k = p^3 - q^3 - r^3, where p, q, r are positive integers satisfying p = q + r.

6, 18, 36, 48, 60, 90, 126, 144, 162, 168, 210, 216, 252, 270, 288, 330, 360, 378, 384, 396, 468, 480, 486, 540, 546, 594, 630, 720, 750, 792, 816, 858, 918, 924, 972, 990, 1008, 1026, 1140, 1152, 1170, 1260, 1296, 1344, 1386, 1404, 1518, 1530, 1560, 1620, 1638, 1656, 1680, 1728, 1800

Offset

1,1

Comments

An alternative representation of k is k = 3*q*r*(q+r), with q, r positive integers, then k is a multiple of 6.

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = 6 * A121741(n).

Example

60 is in the sequence because 60 = 5^3 - 4^3 - 1^3, with 5 = 4 + 1.

Prog

(PARI) ok(n) = {my(i=1, a=0, m=0, j); if(n%6==0, while(a<=n&&m==0, j=1; while(j<i&&m==0, a=3*i*j*(i-j); if(a==n, m=1); j+=1); i+=1)); m}

Crossrefs

Cf. A000578, A003072, A024975, A078129, A255018, A275154.

Sequence in context: A271303 A110965 A111147 * A358843 A328586 A172522

Adjacent sequences: A333818 A333819 A333820 * A333822 A333823 A333824

Keyword

nonn

Author

Antonio Roldán, Apr 06 2020

Status

approved