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A139711 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. 13
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
FORMULA
{k: A000035(A033676(k) + A033677(k)) = 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[120], evdQ] (* Harvey P. Dale, Mar 05 2012 *)
Select[Range[112], IntegerQ[Median[Divisors[#]]] &] (* Stefano Spezia, Mar 14 2023 *)
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
Sequence in context: A039065 A247786 A330565 * A354994 A214585 A196036
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 May 18 15:24 EDT 2024. Contains 372664 sequences. (Running on oeis4.)