OFFSET
1,1
COMMENTS
Observation: a(n) == 0 (mod 12).
Listing primitive tuples (w, x, y, z) enables to compute for some m how many such tuples are in its divisors using the lcm of such tuples. - David A. Corneth, Sep 26 2020
REFERENCES
Y. Perelman, Solutions to x^3 + y^3 + z^3 = u^3, Mathematics can be Fun, pp. 316-9 Mir Moscow 1985.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..504
Fred Richman, Sums of Three Cubes
EXAMPLE
a(3) = 240 because the set of the divisors {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240} contains 3 quadruples {3, 4, 5, 6}, {6, 8, 10, 12} and {12, 16, 20, 24}. The first quadruple is primitive.
MAPLE
with(numtheory):divisors(240);
for n from 1 to 52 do :
ii:=0:
for q from 6 by 6 to 10^8 while(ii=0) do:
d:=divisors(q):n0:=nops(d):it:=0:
for i from 1 to n0-3 do:
for j from i+1 to n0-2 do :
for k from j+1 to n0-1 do:
for m from k+1 to n0 do:
if d[i]^3 + d[j]^3 + d[k]^3 = d[m]^3
then
it:=it+1:
else
fi:
od:
od:
od:
od:
if it = n
then
ii:=1: printf (`%d %d \n`, n, q):
else
fi:
od:
od:
MATHEMATICA
With[{s = Array[Count[Subsets[Divisors[#], {4}]^3, _?(#1 + #2 + #3 == #4 & @@ # &)] &, 10^4]}, Rest@ Values[#][[1 ;; 1 + LengthWhile[Differences@ Keys@ #, # == 1 &] ]] &@ KeySort@ PositionIndex[s][[All, 1]]] (* Michael De Vlieger, Sep 18 2020 *)
PROG
(Python)
from itertools import combinations
from sympy import divisors
def A337098(n):
k = 1
while True:
if n == sum(1 for x in combinations((d**3 for d in divisors(k)), 4) if sum(x[:-1]) == x[-1]):
return k
k += 1 # Chai Wah Wu, Sep 25 2020
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Michel Lagneau, Aug 15 2020
EXTENSIONS
a(13)-a(22) from Chai Wah Wu, Sep 25 2020
More terms from David A. Corneth, Sep 26 2020
STATUS
approved