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Search: id:A132881
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| A132881 |
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a(n) = number of isolated divisors of n. |
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+0
10
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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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 (ogerard(AT)ext.jussieu.fr) Sep 22 2007.
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LINKS
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Ray Chandler, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) = A000005(n) - A132747(n).
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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Table[Length@Select[Divisors[n], (#==1||Mod[n, #-1]>0)&&Mod[n, #+1]>0&], {n, 1, 200}] - Olivier Gerard (ogerard(AT)ext.jussieu.fr) Sep 22 2007.
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CROSSREFS
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Cf. A132882, A132747.
Sequence in context: A057828 A082498 A112223 this_sequence A060130 A008682 A112224
Adjacent sequences: A132878 A132879 A132880 this_sequence A132882 A132883 A132884
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Sep 03 2007
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EXTENSIONS
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More terms from Olivier Gerard (ogerard(AT)ext.jussieu.fr) Sep 22 2007.
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