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Are there more deficient numbers than abundant and perfect numbers?
There are more deficient numbers.
Is any prime number have to be deficient?
All prime numbers are deficient.
Are all prime numbers deficient?
Yes.
Is 63 a deficient number?
All odd numbers with one or two distinct prime factors are deficient. Since 3 and 7 are factors of 63, it must be deficient.
List all deficient numbers up to 100?
1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,21,21,23,25,26,27,29,31,32,33,34,35,37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,61
Is number 11 an abundant and why?
No. All prime numbers are deficient.
Is the number 10 deficient?
Yes. The proper factors of 10 are 1, 2 & 5 with sum 1 + 2 + 5 = 8 which is less than 10, so 10 is deficient.
Are all deficint numbers odd numbers?
No. From Wikipedia: "The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, ..." As you can see, the list includes both even and odd numbers. For example, all powers of two are deficient.
Are all deficient numbers odd numbers?
no, 945 is the first abundant odd number though
How do you show 9 as a deficient number?
Deficient number From Wikipedia, the free encyclopediaIn mathematics, a deficient number or defective number is a number n for which σ(n) < 2n. Here σ(n) is the sum-of-divisors function: the sum of all positive divisors of n, including nitself. An equivalent definition is that the sum of all proper divisors of the number (divisors other than the number itself) is less than the number. The value 2n − σ(n) is called the deficiency of n.The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, … (sequence A005100 in OEIS)As an example, consider the number 21. Its divisors are 1, 3, 7 and 21, and their sum is 32. Because 32 is less than 2 × 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10.An infinite number of both even and odd deficient numbers exist. For example, all odd numbers with one or two distinct prime factors, and all proper divisors of deficient or perfect numbers are deficient.Closely related to deficient numbers are perfect numbers with σ(n) = 2n, and abundant numbers with σ(n) > 2n. The natural numbers were first classified as either deficient, perfect or abundant byNicomachus in his Introductio Arithmetica (circa 100).
Do you think there more perfect than deficient or abundant numbers?
The answer will depend on where "there" is.
Can an Abundant number be a prime number?
No, all prime numbers are deficient.
