If the sum of divisors of a number, excluding that number is equal to that number then that number is called Perfect Number.
6, 28,
496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
= 2^4(2^5 – 1)
Next No. 8128 = 2^6 ×(2^7-1)
33550336 = 2^12 ×(2^13-1)
Perfect number can be represented as 2^(n – 1)× (2^n – 1)
Another property of perfect number is
The sum of reciprocals of the divisors of a perfect number, including that of its own is always = 2.
e.g. for 28
1/1 + 1/2+ 1/4 +1/7 +1/14 / +1/28 = 2
Edit : divisors of 120 are 1, 2, 3, 4 , 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Sum of 1, 2, 3, 4 , 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, is not equal to 120 so it is not a perfect number.
2007-09-07 04:29:38
·
answer #1
·
answered by Pranil 7
·
1⤊
0⤋
The definition of a Perfect Number :: If the sum of divisors of a number, excluding that number is equal to that number then that number is called Perfect Number.
Perfect number can be represented as 2^(n – 1)× (2^n – 1)
where n = no. of term
so, in this formula if u put n = 1 then u will get,
2^(1-1)*(2^1-1) which is nothing but 1. So, the first perfect no. is 1. But it doesn't satisfy its definition. So, we can neglect 1 as a perfect no. .
now, if u put n = 2 in that formula u will get the second perfect no. that is nothing but 6.
if u put n = 3 then u will get the third perfect no. i.e. 28.
So, in this way if u put the value of n sequentially then u would be able to get ur desired answer.
Here according to ur question if u put n = 4 in the equation then u will get 120 which is also a perfect no.
Because, 120 = 1 + 2 + 4 + 8 + 15 + 30 + 60
so, after 28, the next Perfect No. will be 120 [ans]
2007-09-07 16:58:59
·
answer #2
·
answered by sharbadeb 2
·
0⤊
0⤋
It is nothing but wastage of time. What will u get from it ? Ask some purposeful questions .
2007-09-07 04:10:30
·
answer #3
·
answered by abha 4
·
0⤊
0⤋