How Many Amicable Numbers Are There?

Are 1184 and 1210 amicable numbers?

1184 = 1+2+5+10+11+22+55+110+121+242+605, the sum of the divisors of 1210.

In researching this puzzle, it turns out that numbers are amicable if there are two that sum to each other’s proper divisors; they are social numbers if they sum not as a pair, but as a chain, like: 12496, 14288, 15472, 14536, 14264..

What’s a perfect number in math?

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.

How many divisors does 60 have?

60 (number)← 59 60 61 →Factorization22 × 3 × 5Divisors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60Greek numeralΞ´Roman numeralLX8 more rows

Are there any odd perfect numbers?

Like Frenicle, Euler also considered odd perfect numbers. … To this day, it is not known if any odd perfect numbers exist, although numbers up to. have been checked without success, making the existence of odd perfect numbers appear unlikely (Ochem and Rao 2012).

Who is called friend of numbers in mathematics?

The eccentric British mathematician G.H. Hardy is known for his achievements in number theory and mathematical analysis. But he is perhaps even better known for his adoption and mentoring of the self-taught Indian mathematical genius, Srinivasa Ramanujan.

What is an example of a friendly number?

An addition/subtraction strategy that uses a number that is easy to work from, typically 10 or a multiple of 10. For example, to solve 16 – 9, one might recognize that the friendly number 10 is 6 less than 16, then count down 1 more to 9 to find that the difference is 7.

Are 60 and 84 Amicable numbers?

Amicable Numbers The Greeks considered the pair of numbers 220 and 284 to be amicable or friendly numbers because the sum of the proper divisors of one of the numbers is the other number. a. 60 and 84 are amicable numbers.

What are amicable numbers used for?

role in Iamblichus’ studies …“amicable numbers”: two numbers are amicable if each is equal to the sum of the proper divisors of the other (for example, 220 and 284). Attributing virtues such as friendship and justice to numbers was characteristic of the Pythagoreans at all times.

What is a number divisible by 3?

Numbers Divisible by 3. Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3. For example, the sum of the digits for the number 3627 is 18, which is evenly divisible by 3 so the number 3627 is evenly divisible by 3.

IS 220 a perfect number?

The sum of the divisors is 6. Amicable numbers occur in pairs where the sum of the divisors of one number equals a second number and the sum of the divisors of that number equals the first number. An example pair is 220 and 284….Amicable and perfect numbers.NumberSum of factorsType66Perfect2828Perfect220284Amicable284220Amicable10 more rows•May 24, 2016

Is 1 a proper divisor?

itself. Thus, prime numbers have exactly one proper divisor, 1, and every other number has at least two proper divisors.

Is 496 a amicable number?

A perfect number is a cycle of length 1 of s, i.e., a number whose positive divisors (except for itself) sum to itself. For example, 6 is perfect (1+2+3=6), and in fact 6 is the smallest perfect number. The next two perfect numbers are 28 (1+2+4+7+14=28) and 496 (1+2+4+8+16+31+62+124+248=496).

How do you find an amicable number?

Two numbers are said to be amicable if each number is the sum of the proper divisors of the other. A proper divisor of a number is any divisor of the number except the number itself. For example, the proper divisor of 12 are 1, 2, 3, 4, and 6.

Why is 28 the perfect number?

A number is perfect if all of its factors, including 1 but excluding itself, perfectly add up to the number you began with. 6, for example, is perfect, because its factors — 3, 2, and 1 — all sum up to 6. 28 is perfect too: 14, 7, 4, 2, and 1 add up to 28.

How do I find friendly numbers?

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.