A272174 Values of a^3 + b^3 such that the equation a^3 + b^3 = x^2 + y^2 + z^2 is not soluble where a, b > 0 and x, y, z >= 0.

28, 351, 407, 559, 855, 1008, 1343, 1792, 2071, 3087, 3383, 3439, 3591, 3887, 4375, 4439, 5103, 5488, 6119, 6175, 7471, 8343, 9207, 10864, 10991, 11375, 11772, 12175, 12231, 12383, 12636, 12679, 13167, 13895, 14023, 14167, 14364, 14911, 16263, 16956, 17199, 17919, 17999

Offset

1,1

Comments

Intersection of A003325 and A004215.

The first term that occurs in two or more different ways is 515375 = 15^3 + 80^3 = 54^3 + 71^3. - Robert Israel, May 18 2026

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

28 is a term because 28 = 1^3 + 3^3 and 28 is the sum of 4 but no fewer nonzero squares.

Maple

N:= 20000: # for terms <= N
R:= {}:
for a from 1 while 2*a^3 <= N do
  R:= R union select(filter, {seq(a^3 + b^3, b=a .. floor((N-a^3)^(1/3)))})
od:
sort(convert(R, list)); # Robert Israel, May 18 2026

Prog

(PARI) isA004215(n) = {local(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0); }
isA003325(n) = {for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1)); }
lista(nn) = for(n=1, nn, if(isA004215(n) && isA003325(n), print1(n, ", ")));

Crossrefs

Cf. A003325, A004215, A267702.

Sequence in context: A285739 A010833 A022720 * A173421 A085744 A163719

Adjacent sequences: A272171 A272172 A272173 * A272175 A272176 A272177

Keyword

nonn,easy

Author

Altug Alkan, Apr 21 2016

Status

approved