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The proper divisors of 32 are 1, 2, 4, 8, and 16. They add up to 31, so 32 is deficient.

Q: Is the number 32 an abundant deficient or perfect number?

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Deficient number From Wikipedia, the free encyclopediaIn mathematics, a deficient number or defective number is a number n for which Ïƒ(n) < 2n. Here Ïƒ(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 âˆ’ Ïƒ(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, â€¦ (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 Ã— 21, the number 21 is deficient. Its deficiency is 2 Ã— 21 âˆ’ 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 Ïƒ(n) = 2n, and abundant numbers with Ïƒ(n) > 2n. The natural numbers were first classified as either deficient, perfect or abundant byNicomachus in his Introductio Arithmetica (circa 100).

32 is not Perfect.

No.

No. The proper divisors of 32 are 1, 2, 4, 8, and 16. Their sum, 1 + 2 + 4 + 8 + 16 = 31, which is less than 32, so it is not an abundant number.

No, because 32 is not a perfect square.

Related questions

Deficient. The sum of its proper factors is 1+2+4+8+16+32+64+128+256+512 = 1023. Since that sum is less than 1024, it is deficient.

no

They refer to the sum of a number's proper divisors, defined here as all of the factors except the number itself.a perfect number equals the sum of its proper divisorsa deficient number is greater than the sum of its proper divisorsan abundant number is less than the sum of its proper divisors

Deficient number From Wikipedia, the free encyclopediaIn mathematics, a deficient number or defective number is a number n for which Ïƒ(n) < 2n. Here Ïƒ(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 âˆ’ Ïƒ(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, â€¦ (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 Ã— 21, the number 21 is deficient. Its deficiency is 2 Ã— 21 âˆ’ 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 Ïƒ(n) = 2n, and abundant numbers with Ïƒ(n) > 2n. The natural numbers were first classified as either deficient, perfect or abundant byNicomachus in his Introductio Arithmetica (circa 100).

32 is not Perfect.

32+16+8+4+2+1=63. 64 is deficient.

No.

No. The proper divisors of 32 are 1, 2, 4, 8, and 16. Their sum, 1 + 2 + 4 + 8 + 16 = 31, which is less than 32, so it is not an abundant number.

How about: 32*32 = 1024

No, because 32 is not a perfect square.

16 2*16 = 32

Yes. The only known almost perfect numbers are the powers of 2. 32 = 2^5 is an almost perfect number. It has not yet been proved whether {x: x = 2^n for n in N} = {x: x is an almost perfect number}.