A396105 Numbers k such that there are no solutions to A048050(x) + A048050(x+k) = k.

1, 3, 4, 11, 13, 17, 23, 29, 37, 43, 47, 51, 58, 67, 71, 73, 79, 97, 103, 109, 131, 134, 159, 161, 163, 181, 203, 221, 263, 289, 293, 317, 321, 323, 332, 337, 363, 371, 381, 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

Offset

1,2

Comments

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.

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.

Links

Table of n, a(n) for n=1..64.

Maple

g:= proc(n) NumberTheory:-sigma(n)-n-1 end proc:
g(1):= 0:
filter:= proc(n) local x, t;
   for x from 1 to n^2   do
     t:= g(x+n);
     if t > n then next fi;
     if g(x) + t = n then return false fi
  od;
true
end proc:
select(filter, [$1..800]);

Crossrefs

Cf. A048050.

Sequence in context: A098377 A075646 A133621 * A216558 A049619 A295067

Adjacent sequences: A396100 A396102 A396104 * A396106 A396107 A396109

Keyword

nonn

Author

Robert Israel, May 17 2026

Status

approved