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 A139711 A number n is included if the sum of (the largest divisor of n that is <= sqrt(n)) and (the smallest divisor of n that is >= sqrt(n)) is even. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA {n: A000035(A033676(n) + A033677(n)) = 0}. - R. J. Mathar, May 11 2008 EXAMPLE 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. MAPLE 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 MATHEMATICA evdQ[n_]:=Module[{divs=Divisors[n], sr=Sqrt[n]}, EvenQ[Max[Select[divs, #<=sr&]]+Min[Select[divs, #>=sr&]]]]; Select[Range, evdQ] (* Harvey P. Dale, Mar 05 2012 *) PROG (PARI) A063655(n) = {local(d); d=divisors(n); d[(length(d)+1)\2] + d[length(d)\2+1]}; for(n=1, 120, if(A063655(n)%2==0, print1(n, ", ")) ) \\ G. C. Greubel, May 31 2019 CROSSREFS Cf. A063655, A139710. Sequence in context: A039065 A247786 A330565 * A214585 A196036 A081376 Adjacent sequences:  A139708 A139709 A139710 * A139712 A139713 A139714 KEYWORD nonn AUTHOR Leroy Quet, Apr 30 2008 EXTENSIONS More terms from R. J. Mathar, May 11 2008 STATUS approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)