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Variation on betrothed numbers.
0

%I #11 Apr 17 2017 23:32:54

%S 6160,11697,12220,16005,23500,28917,68908,76245,249424,339825,425500,

%T 434784,570405,649990,660825,678376,697851,871585,1017856,1077336,

%U 1238380,1252216,1340865,1483785,1568260,1754536,1823925,1899261,2067625,2166136,2362360,2479065

%N Variation on betrothed numbers.

%C Members of a pair (x,y) such that sigma(x) = sigma(y) = x + y - 1, where sigma = A000203.

%C The first time a pair ordered by its first element is not adjacent is x = 425500, y = 570405 which correspond to a(11) and a(13), respectively.

%F A007992 U A015630.

%e sigma(6160) = sigma(11697) = 6160 + 11697 - 1 = 17856.

%p with(numtheory): P:=proc(q) local a,b,n; for n from 1 to q do

%p a:=sigma(n)-n+1; b:=sigma(a)-a+1; if b=n and a<>b then print(n);

%p fi; od; end: P(10^9);

%Y Cf. A000203, A005276, A007992, A015630.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Apr 13 2017