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 A337098 Least k whose set of divisors contains exactly n quadruples (x, y, z, w) such that x^3 + y^3 + z^3 = w^3, or 0 if no such k exists. 1
 60, 120, 240, 432, 960, 360, 3840, 1728, 2592, 720, 1800, 2520, 161700, 1440, 6840, 9000, 2160, 2880, 168300, 5040, 41472, 5760, 1520820, 4320, 7200, 11520, 119700, 10080, 682080, 10800, 8640, 14400, 27360, 12960, 373248, 20160, 61560, 17280, 28800, 55440, 171000, 21600 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A027750, A095868, A095867, A096545, A096546, A328204, A328149, A331365. Sequence in context: A309842 A177871 A334382 * A252953 A309315 A275339 Adjacent sequences:  A337095 A337096 A337097 * A337099 A337100 A337101 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

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Last modified April 20 20:26 EDT 2021. Contains 343137 sequences. (Running on oeis4.)