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 A132631 Numbers n such that sigma(n+1)-n-1 divides sigma(n)-n, where sigma(n) is sum of positive divisors of n. 1

%I

%S 2,4,6,10,12,16,18,20,22,24,28,30,36,40,42,46,52,58,60,66,70,72,78,82,

%T 88,94,96,100,102,106,108,112,120,126,130,136,138,148,150,156,162,166,

%U 172,178,180,190,192,196,198

%N Numbers n such that sigma(n+1)-n-1 divides sigma(n)-n, where sigma(n) is sum of positive divisors of n.

%C Only even numbers.

%e n=94 -> sigma(n)-n=1+2+47=50 sigma(n+1)-n-1=1+5+19=25 -> 50/25=2

%e n=120 -> sigma(n)-n=1+2+3+4+5+6+8+10+12+15+20+24+30+40+60=240 sigma(n+1)-n-1=1+11=12 -> 240/12=20

%p with(numtheory); P:=proc(n) local a,i; for i from 1 by 1 to n do if sigma(i)-i>0 then a:=(sigma(i)-i)/(sigma(i+1)-i-1); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(200)

%Y Cf. A132585, A132586, A132630.

%K easy,nonn

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 27 2007

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