Question: Who Invented Amicable Numbers?

When did amicable numbers come to Europe?

No pairs of amicable numbers other than 220 and 284 were discovered by European mathematicians until 1636, when French mathematician Pierre de Fermat (1601–1665) found the pair 18, 496 and 17, 296..

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?

…“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).

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.

How many amicable numbers are there?

Altogether there are 42 pairs of amicable numbers below 106.

IS 284 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 factorsType2828Perfect220284Amicable284220Amicable496496Perfect10 more rows•May 24, 2016

Is 1 a proper divisor?

whose only proper divisor is 1 is called a prime number. Equivalently, a prime number is a positive integer that has exactly two positive factors: 1 and itself.

Why Is 9 the perfect number?

The number 9 is revered in Hinduism and considered a complete, perfected and divine number because it represents the end of a cycle in the decimal system, which originated from the Indian subcontinent as early as 3000 BC. … Nine is a significant number in Norse Mythology.

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.

What is the most special number?

6174 is a harshad number, since it is divisible by the sum of its digits: 6174 is a 7-smooth number, i.e. none of its prime factors are greater than 7.

What are special numbers?

Special Numbers in Java are ones whose sum of factorials of digits is equal to the number itself. It can be an N digit number. The program has to first break the number into its corresponding digits and calculate their factorials. … If the sum matches the original number then the number is called to be a Special number.

Why is 6 a special number?

Their arithmetica had a theory of special classes of numbers. … The Greeks called a number such as 6 or 28 a perfect number because the sum of the proper divisors in each case is equal to the number; the proper divisors of 6 are 1, 2, and 3, and their sum is 6.

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.

What are the first 3 perfect numbers?

The first few perfect numbers are 6, 28, 496 and 8128 (sequence A000396 in the OEIS).

What does the number 28 symbolize?

The number 28 symbolizes balance, harmony, service to others, empathy, adaptability, divine life purpose and soul mission, manifestation of wealth, prosperity and abundance, solving problems, achieving success, knowledge, inner wisdom, the Universal Spiritual Law of Karma, partnerships, authority, finances, leadership, …

Are 1184 and 1210 amicable numbers?

Almost perfect number pairs are pairs of numbers that equal the sum of their partner’s divisors. For example, 1184 and 1210 are an almost perfect number pair. 1184 = 1+2+5+10+11+22+55+110+121+242+605, the sum of the divisors of 1210. … The set of numbers requested, above, are amicable numbers if they come in pairs.

Which of the following pairs of numbers is amicable?

, is called the pair sum. The first few amicable pairs are (220, 284), (1184, 1210), (2620, 2924) (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), … (OEIS A002025 and A002046).

Is 1 an amicable number?

Note: 220 and 284 are examples of amicable numbers. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which sum to 284, while the factors of 284 are 1, 2, 4, 71, and 142, which sum to 220.