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# A positive integer n is a perfect number provided that the sum of all

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Joined: 20 Jul 2018
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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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02 Sep 2018, 19:41
Factors of 28 are 1,28,2,14,4 and 7
So sum of their reciprocals is
1+1/28+1/2+1/14+1/4+1/7
28/28+1/28+14/28+2/28+7/28+4/28
(28+1+14+2+7+4)/28
56/28
2

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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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20 Dec 2018, 02:06
Bunuel wrote:
Ndkms wrote:
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

A) 1/4
B) 56/27
C) 2
D) 3
E) 4

Can somebody explain what the question asks and gives ? Is quite convoluted I would say.

A perfect number is a positive integer if the sum of its factors equals twice that number. For example, 6 is a perfect number because the sum of the factors of 6 (which are 1, 2, 3, and 6) is 6*2 = 12: 1 + 2 +3 + 6 = 12.

We are given another perfect number 28 and asked to find the sum of the reciprocals of its factors, so to find 1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28.

Hope it's clear.

What is the purpose of giving the info about 2n here? Its not been used anywhere in calculation of question. (perhaps just to see if we have all the factors?)
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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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09 Sep 2019, 11:57
Quote:
Anantz[/url] , not far fetched. Quite the opposite: spot on. You are correct. And a brainiac. Kudos.

(I am still a learner, too. I looked it up.)

generis
So the sum of the reciprocals of all the positive factors of the perfect numbers such as 6,28,496 and so on will always be 2. Correct?
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A positive integer n is a perfect number provided that the sum of all  [#permalink]

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09 Sep 2019, 15:17
TheNightKing wrote:
Quote:
Anantz[/url] , not far fetched. Quite the opposite: spot on. You are correct. And a brainiac. Kudos.

(I am still a learner, too. I looked it up.)

generis
So the sum of the reciprocals of all the positive factors of the perfect numbers such as 6,28,496 and so on will always be 2. Correct?

TheNightKing , yes, correct.
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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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09 Sep 2019, 16:09
Quote:
TheNightKing , yes, correct.

Thank you!
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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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14 Sep 2019, 11:09
nycgirl212 wrote:
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

A) 1/4
B) 56/27
C) 2
D) 3
E) 4

distinct factors of 28 ; 2^2*7^1 ; (6 factors) i.e 1,2,4,7,14,28
now sum of reciprocals ; 1+1/2+1/4+1/7+1/28 ; 56/28 ; 2
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Re: A positive integer n is a perfect number provided that the sum of all  [#permalink]

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17 Nov 2019, 11:42

You actually don't need to use the first statement.

A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

n: sum of factors=2n
n=28 then sum of 1/factors =?

Factors=1,2,4,7,14, and 28

Sum of reciprocals= 1/1+1/2+1/4+1/7+1/14+1/28
= (28+14+7+4+2+1)/28
=2*28/28 =2

nycgirl212 wrote:
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28?

A) 1/4
B) 56/27
C) 2
D) 3
E) 4
Re: A positive integer n is a perfect number provided that the sum of all   [#permalink] 17 Nov 2019, 11:42

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