

A138652


Consider the differences between adjacent divisors (ordered by size) of (2n). a(n) = the number of such differences that are divisors of (2n).


1



1, 2, 3, 3, 2, 5, 2, 4, 5, 5, 2, 7, 2, 4, 6, 5, 2, 8, 2, 6, 7, 4, 2, 9, 3, 4, 7, 5, 2, 11, 2, 6, 6, 4, 3, 11, 2, 4, 6, 7, 2, 10, 2, 6, 10, 4, 2, 11, 3, 8, 6, 6, 2, 11, 5, 6, 6, 4, 2, 15, 2, 4, 9, 7, 4, 9, 2, 6, 6, 8, 2, 14, 2, 4, 9, 6, 2, 11, 2, 8, 9, 4, 2, 15, 4, 4, 6, 6, 2, 17, 3, 6, 6, 4, 4, 13, 2, 6, 9
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OFFSET

1,2


COMMENTS

For n = any odd positive integer, there are no differences (between consecutive divisors of n) that divide n.
a(n) + A060763(2n) = A000005(2n)1.


LINKS

Table of n, a(n) for n=1..99.


MAPLE

A138652 := proc(n) local a, dvs, i ; a := 0 ; dvs := sort(convert(numtheory[divisors](2*n), list)) ; for i from 2 to nops(dvs) do if (2*n) mod ( op(i, dvs)op(i1, dvs) ) = 0 then a := a+1 ; fi ; od: a ; end: seq(A138652(n), n=1..120) ; # R. J. Mathar, May 20 2008


MATHEMATICA

a = {}; For[n = 2, n < 200, n = n + 2, b = Table[Divisors[n][[i + 1]]  Divisors[n][[i]], {i, 1, Length[Divisors[n]]  1}]; AppendTo[a, Length[Select[b, Mod[n, # ] == 0 &]]]]; a (* Stefan Steinerberger, May 18 2008 *)


CROSSREFS

Cf. A060763.
Cf. A060741.
Sequence in context: A034799 A008985 A326699 * A323833 A131899 A095174
Adjacent sequences: A138649 A138650 A138651 * A138653 A138654 A138655


KEYWORD

nonn


AUTHOR

Leroy Quet, May 15 2008


EXTENSIONS

More terms from Stefan Steinerberger and R. J. Mathar, May 18 2008


STATUS

approved



