

A139710


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 odd.


2



2, 6, 10, 12, 14, 18, 20, 22, 26, 28, 30, 34, 38, 40, 42, 44, 46, 50, 52, 54, 56, 58, 62, 66, 68, 70, 72, 74, 76, 78, 82, 84, 86, 88, 90, 92, 94, 98, 102, 104, 106, 108, 110, 114, 116, 118, 122, 124, 126, 130, 132, 134, 136, 138, 142, 146, 148, 150, 152, 154, 156, 158
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OFFSET

1,1


COMMENTS

All terms of this sequence are even.
A139711 contains all positive integers not in this sequence and vice versa.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


FORMULA

{n: A000035(A033676(n) + A033677(n)) = 1}.  R. J. Mathar, May 11 2008


EXAMPLE

The divisors of 12 are 1,2,3,4,6,12. The middle 2 divisors are 3 and 4. The sum of these is 7, which is odd. So 12 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: isA139710 := proc(n) RETURN ( ( A033676(n)+A033677(n) ) mod 2 = 1 ) ; end: for n from 1 to 300 do if isA139710(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, May 11 2008


MATHEMATICA

centralDivisors:=#[[({Floor[#], Ceiling[#]}&[(1+#)/2&[Length[#]]])]]&[Divisors[#]]&;
Select[Range[500], OddQ[Total[#]]&[centralDivisors[#]]&](* Peter J. C. Moses, May 31 2019 *)


PROG

(PARI) b(n) = {local(d); d=divisors(n); d[(length(d)+1)\2] + d[length(d)\2+1]};
for(n=1, 180, if(b(n)%2==1, print1(n, ", ")) ) \\ G. C. Greubel, May 31 2019


CROSSREFS

Cf. A063655, A139711.
Sequence in context: A139799 A214586 A305634 * A194712 A057921 A095300
Adjacent sequences: A139707 A139708 A139709 * A139711 A139712 A139713


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 30 2008


EXTENSIONS

More terms from R. J. Mathar, May 11 2008


STATUS

approved



