(sorry about the complete tripe in previous post - the n.sigma(n) eqv. 2 mod

phi(n) is only true for n=p, and n=4,6,22).

--

Continuing Jack's work:

for (n=2,100000,if ((sigma(n-1)+sigma(n)+sigma(n+1))%(n-1)==0,

write("sigmaconn.txt",n,":",sigma(n-1)%(n-1),":",+sigma(n)%(n-1),":",sigma(n

+1)%(n-1),":",(sigma(n-1)+sigma(n)+sigma(n+1)))))

2,3,24,64,227,291,784,1883,7731,18547,25723,30397,94358

for (n=2,100000,if ((sigma(n-1)+sigma(n)+sigma(n+1))%(n+1)==0,

write("sigmaconp.txt",n,":",sigma(n-1)%(n+1),":",+sigma(n)%(n+1),":",sigma(n

+1)%(n+1),":",(sigma(n-1)+sigma(n)+sigma(n+1)))))

8,21,22,23,57,157,505,1053,2147,2273,3311,4679,5931,7898,22682

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A related question - when does sigma(n,2)%sigma(n,1)==0?

If n is a square, and also:

20,50,117,180,200,242,325,450,468,500,578,605,650,800,968,980

for (n=2,10000, if (sigma(n,2)%sigma(n,1)==0 &&

!issquare(n),write("sigmasigmasq.txt",n)))

Anyone spot the missing link?

Jon Perry

perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript

http://www.brainbench.com