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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

Table of n, a(n) for n=1..83.

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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Last modified November 19 07:02 EST 2017. Contains 294915 sequences.