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%I #4 Mar 30 2012 18:50:43
%S 0,0,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,21,0,14,0,0,0,220,0,0,0,0,0,208,0,
%T 0,0,0,0,791,0,0,0,161,0,181,0,0,0,0,0,2330,0,0,0,0,0,181,0,134,0,0,0,
%U 25068,0,0,0,0,0,181,0,0,0,92,0,24243,0,0,0,0,0,181,0,1774,0,0,0
%N Number of ways to partition the set of divisors of n into three subsets such that their sums form an integer triangle.
%C a(n) > 0 iff n is abundant; a(A005101(m)) = A091235(m).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbundantNumber.html">Abundant Number</a>
%e Set of divisors of n=12: {1,2,3,4,6,12}, a(12)=20:
%e [12+1,6+4+3,2], [12+1,6+4+2,3], [12+1,6+3+2,4], [12+1,6+4,3+2],
%e [12+1,6+3,4+2], [12+1,6+2,4+3], [12+1,6,4+3+2], [12,6+4+3,2+1],
%e [12,6+4+2+1,3], [12,6+4+2,3+1], [12,6+3+2+1,4], [12,6+4+1,3+2],
%e [12,6+3+2,4+1], [12,6+4,3+2+1], [12,6+3+1,4+2], [12,6+3,4+2+1],
%e [12,6+2+1,4+3], [12,6+2,4+3+1], [12,6+1,4+3+2] and [12,6,4+3+2+1].
%e set of divisors of n=20: {1,2,4,5,10,20}, a(20)=14:
%e [20,10+5+4+1,2], [20,10+5+4,2+1], [20,10+5+2+1,4], [20,10+5+2,4+1],
%e [20,10+4+2+1,5], [20,10+5+1,4+2], [20,10+4+2,5+1], [20,10+5,4+2+1],
%e [20,10+4+1,5+2], [20,10+4,5+2+1], [20,10+2+1,5+4], [20,10+2,5+4+1],
%e [20,10+1,5+4+2] and [20,10,5+4+2+1].
%K nonn
%O 1,12
%A _Reinhard Zumkeller_, Dec 27 2003
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