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/sci/ - Science & Math

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2644632 No.2644632 [Reply] [Original]

Is 10 a solitary number?

>A number that belongs to a singleton club, because no other number is friendly with it, is a solitary number. All prime numbers are known to be solitary, as are powers of prime numbers. More generally, if the numbers n and σ(n) are coprime – meaning that the greatest common divisor of these numbers is 1, so that σ(n)/n is an irreducible fraction – then the number n is solitary. For a prime number p we have σ(p) = p + 1, which is coprime with p.


Sorry if this is dumb, its 2 AM.

>> No.2644658
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2644658

Waiting patiently

>> No.2644692

well, ten isn't a prime number, so I would say no

unless for some reason you're using binary...

then uh, I don't know

>> No.2645125

I think σ(n) is the sum of the divisors of n including n. So σ(10) = 1+2+5+10 = 18. Now 10 and 18 are not coprime. Nor is it a prime or a power of a prime, so it is not solitary.