1,12

a(n) > 0 iff n is abundant; a(A005101(m)) = A091235(m).

Eric Weisstein's World of Mathematics, Abundant Number

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].

Sequence in context: A137643 A023921 A072840 this_sequence A070708 A084029 A008426

Adjacent sequences: A091231 A091232 A091233 this_sequence A091235 A091236 A091237

nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 27 2003