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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: A351570 A023921 A072840 * A221873 A278073 A365912
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Dec 27 2003
STATUS
approved

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Last modified June 25 13:13 EDT 2024. Contains 373705 sequences. (Running on oeis4.)