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%I #6 May 20 2017 13:02:36
%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.
%H Harvey P. Dale, <a href="/A132631/b132631.txt">Table of n, a(n) for n = 1..1000</a>
%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)
%t Select[Range[2,200],Divisible[DivisorSigma[1,#]-#,DivisorSigma[1,#+1]-#-1]&] (* _Harvey P. Dale_, May 20 2017 *)
%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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