- Jul 1 1:23 PMA swerve.

Can you explain why sigma(n-1)+sigma(n)+sigma(n+1) is nearly always even?

(PARI/GP)

for (n=2,1000,write("sigmax.txt",(sigma(n-1)+sigma(n)+sigma(n+1))%2))

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry/maths

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-----Original Message-----

From: Markus Frind [mailto:flames@...]

Sent: 01 July 2002 02:35

To: primenumbers@yahoogroups.com

Subject: [PrimeNumbers] Factor patterns

Given 12n-1 is it possible to prove that all factors of 12n-1 add up to

12*k ? Note this breaks down when you have more then 2 factors, but if

you if you limit yourself to 2 factors (prime or composite) it works. The

same also holds true for 6n-1 does this have to do with the fact that all

primes can be expressed as either 6k-1 or 6k+1 ?

12*45 -1 = 7 * 7 *11

49 + 11 = 60

7 + 77 = 84

12*8-1 = 95

19+5 = 24

etc

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