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A328204
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Numbers of quadruples contained in the divisors of A328149(n).
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4
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1, 1, 2, 2, 2, 2, 3, 3, 2, 6, 2, 4, 4, 2, 3, 4, 4, 3, 2, 10, 2, 2, 4, 6, 4, 2, 5, 4, 2, 10, 2, 5, 6, 2, 4, 6, 4, 2, 2, 14, 3, 4, 4, 4, 4, 2, 6, 1, 8, 2, 11, 2, 4, 6, 4, 4, 6, 4, 2, 4, 17, 2, 2, 4, 6, 4, 4, 1, 8, 4, 2, 12, 2, 9, 6, 2, 6, 4, 4, 4, 2, 18, 3, 2, 6
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OFFSET
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1,3
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COMMENTS
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A quadruple (x, y, z, w) of A328149 is a set of positive integers that satisfy x^3 + y^3 + z^3 = w^3.
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LINKS
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EXAMPLE
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a(7) = 3 because the set of divisors of A328149(7) = 240: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240} contains the three quadruples {3, 4, 5, 6}, {6, 8, 10, 12} and {12, 16, 20, 24}. The first quadruple is primitive.
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MAPLE
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with(numtheory):
for n from 3 to 3000 do :
d:=divisors(n):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>0 then
printf(`%d, `, it):
else fi:
od:
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MATHEMATICA
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nq[n_] := If[Mod[n, 6] > 0, 0, Block[{t, u, v, c = 0, d = Divisors[n], m}, m = Length@ d; Do[t = d[[i]]^3 + d[[j]]^3; Do[u = t + d[[h]]^2; If[u > n^3, Break[]]; If[Mod[n^3, u] == 0 && IntegerQ[v = u^(1/3)] && Mod[n, v] == 0, c++], {h, j+1, m-1}], {i, m-3}, {j, i+1, m - 2}]; c]]; Select[Array[nq, 1638], # > 0 &] (* program from Giovanni Resta adapted for the sequence. See A330894 *)
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PROG
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(PARI) isok(n) = {my(d=divisors(n), nb=0, m); if (#d > 3, for (i=1, #d-3, for (j=i+1, #d-2, for (k=j+1, #d-1, if (ispower(d[i]^3+d[j]^3+d[k]^3, 3, &m) && !(n%m), nb++); ); ); ); ); nb; }
lista(nn) = my(m); for (n=1, nn, if (m=isok(n), print1(m, ", "))); \\ Michel Marcus, Nov 15 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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