|
| |
|
|
A132881
|
|
a(n) = number of isolated divisors of n.
|
|
10
| |
|
|
1, 0, 2, 1, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 4, 3, 2, 3, 2, 2, 4, 2, 2, 4, 3, 2, 4, 4, 2, 3, 2, 4, 4, 2, 4, 5, 2, 2, 4, 4, 2, 3, 2, 4, 6, 2, 2, 6, 3, 4, 4, 4, 2, 5, 4, 4, 4, 2, 2, 6, 2, 2, 6, 5, 4, 5, 2, 4, 4, 6, 2, 6, 2, 2, 6, 4, 4, 5, 2, 6, 5, 2, 2, 6, 4, 2, 4, 6, 2, 5, 4, 4, 4, 2, 4, 8, 2, 4, 6, 5, 2, 5, 2, 6, 8
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| A divisor d of n is isolated if neither d-1 nor d+1 divides n.
The convention for 1 is that it is an isolated divisor iff n is odd. - Olivier Gerard (olivier.gerard(AT)gmail.com) Sep 22 2007.
|
|
|
LINKS
| Ray Chandler, Table of n, a(n) for n=1..10000
|
|
|
FORMULA
| a(n) = A000005(n) - A132747(n).
|
|
|
EXAMPLE
| The positive divisors of 56 are: 1,2,4,7,8,14,28,56. Of these, 1 and 2 are adjacent and 7 and 8 are adjacent. The isolated divisors are therefore 4,14, 28,56. There are 4 of these, so a(56) = 4.
|
|
|
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, seq(nops(a(j)), j=3..105); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 02 2007
|
|
|
MATHEMATICA
| Table[Length@Select[Divisors[n], (#==1||Mod[n, #-1]>0)&&Mod[n, #+1]>0&], {n, 1, 200}] - Olivier Gerard (olivier.gerard(AT)gmail.com) Sep 22 2007.
|
|
|
CROSSREFS
| Cf. A132882, A132747.
Sequence in context: A112223 A178771 A193929 * A060130 A008682 A112224
Adjacent sequences: A132878 A132879 A132880 * A132882 A132883 A132884
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Leroy Quet, Sep 03 2007
|
|
|
EXTENSIONS
| More terms from Olivier Gerard (olivier.gerard(AT)gmail.com) Sep 22 2007.
|
| |
|
|
