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A371072 a(n)/144 is the minimum squared volume > 0 of a tetrahedron with the sum of its integer edge lengths equal to n.

%I A371072 #17 Mar 28 2024 18:04:21
%S A371072 11,14,44,26,59,34,47,126,119,62,215,54,107,98,243,146,335,142,191,
%T A371072 614,479,194,764,423,299,254,1004,239,851,322,304,783,887,134,479,
%U A371072 1719,315,234,1196,191,896,574,767,1127,151,674,956,956,671,146,1391,1082,791,898,263,1184,151
%N A371072 a(n)/144 is the minimum squared volume > 0 of a tetrahedron with the sum of its integer edge lengths equal to n.
%C A371072 a(6) = 2, but since there are no tetrahedra with volume > 0 for n=7 and n=8, the offset 9 is chosen.
%H A371072 Hugo Pfoertner, <a href="/A371072/b371072.txt">Table of n, a(n) for n = 9..150</a>
%o A371072 (PARI) a371072(n) = {my (Vmin=oo); forpart (w=n, forperm (w, v, if(v[4]+v[5]<v[6], next); if(v[4]+v[6]<v[5], next); if(v[5]+v[6]<v[4], next); if(v[1]+v[2]<v[4], next); if(v[1]+v[4]<v[2], next); if(v[2]+v[4]<v[1], next); if(v[1]+v[3]<v[5], next); if(v[1]+v[5]<v[3], next); if(v[3]+v[5]<v[1], next); if(v[2]+v[3]<v[6], next); if(v[2]+v[6]<v[3], next); if(v[3]+v[6]<v[2], next); my(CM=matdet ([0, 1, 1, 1, 1; 1, 0, v[1]^2, v[2]^2, v[3]^2; 1, v[1]^2, 0, v[4]^2, v[5]^2; 1, v[2]^2, v[4]^2, 0, v[6]^2; 1, v[3]^2, v[5]^2, v[6]^2, 0])); if (CM>0, Vmin=min(Vmin,CM))), [1, n], [6, 6]); Vmin/2};
%Y A371072 Cf. A097125, A208454, A371070, A371073, A371344.
%Y A371072 Subset of A371071.
%K A371072 nonn
%O A371072 9,1
%A A371072 _Hugo Pfoertner_, Mar 19 2024