OFFSET
1,2
COMMENTS
The sequence is conjectured to be a permutation of the positive integers. In the first 250000 terms there are twenty-three fixed points: 1, 2, 12, 16, 27 ..., 2279, 5401, 7339. It is possibly no more exist although this is unknown.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Scott R. Shannon, Image of the first 250000 terms. The green line is y = n.
EXAMPLE
a(7) = 14 as a(6) = 5 which has two divisors, and 14 is the smallest unused number that shares a factor with 5 + 2 = 7.
MAPLE
A[1]:= 1; S:= {$2..5000}:
for i from 2 do
found:= false;
t:= A[i-1] + numtheory:-tau(A[i-1]);
for s in S do
if igcd(s, t) > 1 then
A[i]:= s;
found:= true;
S:= S minus {s};
break
fi
od;
if not found then break fi;
od:
seq(A[j], j=1..i-1); # Robert Israel, Jan 16 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Aug 07 2022
STATUS
approved