OFFSET
1,2
EXAMPLE
The positive divisors of 56 are: 1,2,4,7,8,14,28,56. Of these, 1 and 2 differ by 1 and 7 and 8 differ by 1. Therefore the isolated divisors of 56 are 4,14,28,56. But 4 is not next to any isolated divisors in the list of all positive divisors of 56. (4 is next to 2 and 7, neither of which is isolated.) So 4 is an isolated isolated divisor of 56 and 56, therefore has at least one isolated isolated divisor.
MAPLE
isIso := proc(k, divs) if not k-1 in divs and not k+1 in divs then true ; else false ; fi ; end: isA131847 := proc(n) local divs, i, isos ; divs := convert(numtheory[divisors](n), list) ; isos := [] ; for i from 1 to nops(divs) do isos := [op(isos), isIso(op(i, divs), divs)] ; od: if nops(isos) = 1 then RETURN(true) ; fi ; if op(1, isos) = true and op(2, isos) = false then RETURN(true) ; fi ; for i from 2 to nops(isos)-1 do if op(i, isos) = true and op(i-1, isos)=false and op(i+1, isos) = false then RETURN(true) ; fi ; od: if op(-1, isos) = true and op(-2, isos) = false then RETURN(true) ; fi ; RETURN(false) ; end: for n from 1 to 1500 do if isA131847(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Oct 24 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Oct 04 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 24 2007
STATUS
approved