OFFSET
1,4
COMMENTS
The second term of the sequence, which corresponds to the second row of the array, is 0 simply as a placeholder, since 2 has no isolated divisors.
The number of terms in the n-th row of the array is A132881(n) (with the exception of row 2, which has 0 elements, but is represented here as 0).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..12248 (Rows 1 <= n <= 2000).
EXAMPLE
The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are adjacent and 4 and 5 are adjacent. So the isolated divisors of 20 are 10 and 20.
Triangle begins:
1
-
1,3
4
1,5
6
1,7
4,8
1,3,9
5,10
1,11
6,12
1,13
7,14
1,3,5,15
4,8,16
...
MAPLE
with(numtheory): a:=proc(n) local div, ISO, i: div:=divisors(n): ISO:={}: for i to tau(n) do if member(div[i]-1, div)=false and member(div[i]+1, div)=false then ISO:=`union`(ISO, {div[i]}) end if end do end proc: 1; 0; for j from 3 to 30 do seq(a(j)[i], i=1..nops(a(j)))end do; # yields sequence in the form of an array - Emeric Deutsch, Oct 02 2007
MATHEMATICA
Table[Select[Divisors@ n, NoneTrue[# + {-1 + 2 Boole[# == 1], 1}, Divisible[n, #] &] &] /. {} -> {0}, {n, 36}] // Flatten (* Michael De Vlieger, Aug 19 2017 *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Leroy Quet, Sep 23 2007
EXTENSIONS
More terms from Emeric Deutsch, Oct 02 2007
Extended by Ray Chandler, Jun 24 2008
STATUS
approved