

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
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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

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[120], 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: A187885 A039065 A247786 * 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



