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Manuals/calci/PERFECTNUMBERS (view source)
Revision as of 08:13, 11 February 2020
, 08:13, 11 February 2020→DEFICIENTNUMBERS
==DEFICIENTNUMBERS==
==DEFICIENTNUMBERS==
*Deficient number is a number <math>n</math> for which the sum of divisors <math>\sigma(n)<2n</math>, or, equivalently, the sum of proper divisors (or aliquot sum) <math>s(n)<n</math>. The value <math>2n</math> − <math>\sigma(n)</math> (or <math>n</math> − <math>s(n)</math>) is called the number's deficiency.
*Deficient number is a number <math>n</math> for which the sum of divisors <math>\sigma(n)<2n</math>, or, equivalently, the sum of proper divisors (or aliquot sum) <math>s(n)<n</math>. The value <math>2n</math> − <math>\sigma(n)</math> (or <math>n</math> − <math>s(n)</math>) is called the number's deficiency.
*Properties of Deficient Numbers are:
*The aliquot sums of prime numbers equal 1, all prime numbers are deficient.
*An infinite number of both even and odd deficient numbers exist.
*All odd numbers with one or two distinct prime factors are deficient.
*All proper divisors of deficient or perfect numbers are deficient.
*Some of the Deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17 and etc.
*DEFICIENTNUMBERS(110) = 2 3 4 5 7 8 9 10 11 13 14 15 16 17 19 21 22 23 25..........
==Examples==
==Examples==