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 A091234 Number of ways to partition the set of divisors of n into three subsets such that their sums form an integer triangle. 1
 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, 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, 25068, 0, 0, 0, 0, 0, 181, 0, 0, 0, 92, 0, 24243, 0, 0, 0, 0, 0, 181, 0, 1774, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS a(n) > 0 iff n is abundant; a(A005101(m)) = A091235(m). LINKS Eric Weisstein's World of Mathematics, Abundant Number EXAMPLE Set of divisors of n=12: {1,2,3,4,6,12}, a(12)=20: [12+1,6+4+3,2], [12+1,6+4+2,3], [12+1,6+3+2,4], [12+1,6+4,3+2], [12+1,6+3,4+2], [12+1,6+2,4+3], [12+1,6,4+3+2], [12,6+4+3,2+1], [12,6+4+2+1,3], [12,6+4+2,3+1], [12,6+3+2+1,4], [12,6+4+1,3+2], [12,6+3+2,4+1], [12,6+4,3+2+1], [12,6+3+1,4+2], [12,6+3,4+2+1], [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]. set of divisors of n=20: {1,2,4,5,10,20}, a(20)=14: [20,10+5+4+1,2], [20,10+5+4,2+1], [20,10+5+2+1,4], [20,10+5+2,4+1], [20,10+4+2+1,5], [20,10+5+1,4+2], [20,10+4+2,5+1], [20,10+5,4+2+1], [20,10+4+1,5+2], [20,10+4,5+2+1], [20,10+2+1,5+4], [20,10+2,5+4+1], [20,10+1,5+4+2] and [20,10,5+4+2+1]. CROSSREFS Sequence in context: A137643 A023921 A072840 * A221873 A278073 A070708 Adjacent sequences:  A091231 A091232 A091233 * A091235 A091236 A091237 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 27 2003 STATUS approved

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