A396105 - OEIS

%I #6 May 18 2026 10:13:10

%S 1,3,4,11,13,17,23,29,37,43,47,51,58,67,71,73,79,97,103,109,131,134,

%T 159,161,163,181,203,221,263,289,293,317,321,323,332,337,363,371,381,

%U 391,401,409,413,463,473,485,535,577,581,599,601,607,623,667,673,687,697,701,713,737,757,767,773,781

%N Numbers k such that there are no solutions to A048050(x) + A048050(x+k) = k.

%C Numbers k such that there is no x where the sum of the nontrivial divisors of x and the nontrivial divisors of x+k is k.

%C If x has any nontrivial divisors, the sum of those divisors is at least sqrt(x).  Thus any solution to A048050(x) + A048050(x+k) is at most x^2.  This means that the search for solutions is finite.

%p g:= proc(n) NumberTheory:-sigma(n)-n-1 end proc:

%p g(1):= 0:

%p filter:= proc(n) local x,t;

%p    for x from 1 to n^2   do

%p      t:= g(x+n);

%p      if t > n then next fi;

%p      if g(x) + t = n then return false fi

%p   od;

%p true

%p end proc:

%p select(filter, [$1..800]);

%Y Cf. A048050.

%K nonn

%O 1,2

%A _Robert Israel_, May 17 2026