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 A131847 Positive integers n which each have at least one "isolated isolated divisor". An isolated isolated divisor is an isolated divisor that is not adjacent to any other isolated divisors in the list of all positive divisors of n. A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n. 0
 1, 4, 6, 56, 72, 110, 112, 132, 144, 156, 182, 210, 216, 224, 288, 380, 392, 432, 440, 448, 506, 550, 576, 616, 648, 720, 728, 780, 784, 792, 864, 880, 896, 924, 936, 952, 1050, 1064, 1152, 1200, 1210, 1224, 1232, 1260, 1274, 1288, 1296, 1320, 1368, 1404 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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 Cf. A133779. Sequence in context: A013024 A012910 A259133 * A351733 A089630 A058162 Adjacent sequences:  A131844 A131845 A131846 * A131848 A131849 A131850 KEYWORD nonn AUTHOR Leroy Quet, Oct 04 2007 EXTENSIONS More terms from R. J. Mathar, Oct 24 2007 STATUS approved

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Last modified September 28 08:13 EDT 2022. Contains 357068 sequences. (Running on oeis4.)