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d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
10 8: Duodecimal: 8 12: ... Sphenic numbers always have exactly eight divisors. [6] 8 is the base of the octal ... "8" is the eighth song on the album When We All ...
In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, = |,. It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.
Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than n. For example, the proper divisors of 8 are 1, 2, and 4, and their sum is less than 8, so 8 is deficient. Denoting by σ(n) the sum of divisors, the value 2n – σ(n) is called the number's deficiency.
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. The first few semiperfect numbers are: 6, 12, 18, 20, 24, 28, 30, 36, 40, ... (sequence A005835 in the ...
"8×10" was released as a single by Decca Records in August 1963. [3] The single spent 23 weeks on the Billboard Hot Country Singles chart, peaking at number two in October 1963. [ 4 ] It was Anderson's third single to place on the Billboard Hot 100 , reaching number 53 around the same time frame.
The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.
This follows since 2 d*(n) divides the sum of the unitary divisors of an odd number n, where d*(n) is the number of distinct prime factors of n. One gets this because the sum of all the unitary divisors is a multiplicative function and one has that the sum of the unitary divisors of a prime power p a is p a + 1 which is even for all odd primes ...