

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
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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



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]};


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



