A139710 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 odd.

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

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

{k: A000035(A033676(k) + A033677(k)) = 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 *)
Select[Range[158], !IntegerQ[Median[Divisors[#]]] &] (* Stefano Spezia, Mar 14 2023 *)

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. A000035, A033676, A033677, A063655, A139711.

Sequence in context: A214586 A337687 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