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Is 20 a friendly number?
There are some numbers that can easily be proved to be solitary, but the status of numbers 10, 14, 15, 20, and many others remains unknown (Hickerson 2002). The numbers known to be friendly are given by 6, 12, 24, 28, 30, 40, 42, 56, 60, (OEIS A074902).
What is a friendly pair in math?
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same “abundancy” form a friendly pair; n numbers with the same “abundancy” form a friendly n-tuple.
What are pairs numbers?
Two together. Often with something in common. Example: {12,7} is a pair of numbers.
How many pairs can you make with 5 numbers?
In total you will find 5 × 24 = 120 possibilities.
Which is a friendly pair of two numbers?
In number theory, friendly pairs are two numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself i.e ? (n)/n. S o, two number n and m are friendly number if
Which is the smallest friendly number 1 through 5?
The numbers 1 through 5 are all solitary. The smallest friendly number is 6, forming for example the friendly pair 6 and 28 with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases.
How are friendly numbers related to amicable numbers?
In spite of the similarity in name, there is no specific relationship between the friendly numbers and the amicable numbers or the sociable numbers, although the definitions of the latter two also involve the divisor function. As another example, 30 and 140 form a friendly pair, because 30 and 140 have the same “abundancy”:
How are two numbers with the same abundancy friendly?
Two numbers with the same “abundancy” form a friendly pair; n numbers with the same “abundancy” form a friendly n-tuple . Being mutually friendly is an equivalence relation, and thus induces a partition of the positive naturals into clubs ( equivalence classes) of mutually “friendly numbers”.