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A139711
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Numbers k such that the sum of (the largest divisor of k that is <= sqrt(k)) and (the smallest divisor of k that is >= sqrt(k)) is even.
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13
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1, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 24, 25, 27, 29, 31, 32, 33, 35, 36, 37, 39, 41, 43, 45, 47, 48, 49, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 80, 81, 83, 85, 87, 89, 91, 93, 95, 96, 97, 99, 100, 101, 103, 105, 107, 109, 111, 112
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OFFSET
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1,2
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COMMENTS
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All odd positive integers and all perfect squares are included in this sequence.
A139710 contains all positive integers not in this sequence and vice versa.
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LINKS
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FORMULA
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EXAMPLE
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The divisors of 24 are 1,2,3,4,6,8,12,24. The middle 2 divisors are 4 and 6. The sum of these is 10, which is even. So 24 is included in the sequence.
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MAPLE
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A033676 := proc(n) local d ; for d from floor(sqrt(n)) to 1 by -1 do if n mod d = 0 then RETURN(d) ; fi ; od: end: A033677 := proc(n) n/A033676(n) ; end: isA139711 := proc(n) RETURN ( ( A033676(n)+A033677(n) ) mod 2 = 0 ) ; end: for n from 1 to 300 do if isA139711(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, May 11 2008
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MATHEMATICA
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evdQ[n_]:=Module[{divs=Divisors[n], sr=Sqrt[n]}, EvenQ[Max[Select[divs, #<=sr&]]+Min[Select[divs, #>=sr&]]]]; Select[Range[120], evdQ] (* Harvey P. Dale, Mar 05 2012 *)
Select[Range[112], IntegerQ[Median[Divisors[#]]] &] (* Stefano Spezia, Mar 14 2023 *)
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PROG
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(PARI) A063655(n) = {local(d); d=divisors(n); d[(length(d)+1)\2] + d[length(d)\2+1]};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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