amiable adj
1. disposed to please; "an amiable villain with a cocky sidelong grin"- Hal Hinson [syn: good-humored, good-humoured]
2. diffusing warmth and friendliness; "an affable smile"; "an amiable gathering"; "cordial relations"; "a cordial greeting"; "a genial host" [syn: affable, cordial, genial]

Amiable \A"mi*a*ble\, a. [F. amiable, L. amicabilis friendly, fr. amicus friend, fr. amare to love. The meaning has been influenced by F. aimable, L. amabilis lovable, fr. amare to love. Cf. Amicable, Amorous, Amability.]
1. Lovable; lovely; pleasing. [Obs. or R.] So amiable a prospect. --Sir T. Herbert.
2. Friendly; kindly; sweet; gracious; as, an amiable temper or mood; amiable ideas.
3. Possessing sweetness of disposition; having sweetness of temper, kind-heartedness, etc., which causes one to be liked; as, an amiable woman.
4. Done out of love. [Obs.] Lay an amiable siege to the honesty of this Ford's wife. --Shak.

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Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive integer divisor other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) A pair of amicable numbers constitutes an aliquot sequence of period 2. A related concept is that of a perfect number, which is a number which equals the sum of its own proper divisors, in other words a number which forms an aliquot sequence of period 1. Numbers that are members of an aliquot sequence with period greater than 2 are known as sociable numbers.

For example, the smallest pair of amicable numbers is (220, 284); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71, and 142, of which the sum is 220.

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