

A356432


a(1) = 1; for n > 1, a(n) is the smallest positive number not occurring earlier that shares a factor with a(n1) plus the number of divisors of a(n1).


3



1, 2, 4, 7, 3, 5, 14, 6, 8, 9, 10, 12, 15, 19, 18, 16, 21, 20, 13, 24, 22, 26, 25, 28, 17, 38, 27, 31, 11, 39, 43, 30, 32, 34, 36, 33, 37, 42, 35, 45, 48, 29, 62, 40, 44, 46, 50, 49, 52, 54, 56, 58, 60, 51, 55, 59, 61, 57, 122, 63, 23, 65, 66, 64, 71, 73, 69, 146, 68, 70, 72, 74, 75, 78, 76, 41
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence is conjectured to be a permutation of the positive integers. In the first 250000 terms there are twentythree fixed points: 1, 2, 12, 16, 27 ..., 2279, 5401, 7339. It is possibly no more exist although this is unknown.


LINKS



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[i1] + numtheory:tau(A[i1]);
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:


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



