A060741 Number of divisors of 2n which are also differences between consecutive divisors of 2n (ordered by size).

1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 2, 4, 2, 4, 4, 5, 2, 5, 2, 4, 4, 4, 2, 5, 3, 4, 4, 4, 2, 7, 2, 6, 4, 4, 3, 6, 2, 4, 4, 5, 2, 5, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 7, 4, 4, 4, 4, 2, 9, 2, 4, 5, 7, 4, 5, 2, 6, 4, 6, 2, 8, 2, 4, 6, 6, 2, 6, 2, 6, 5, 4, 2, 8, 4, 4, 4, 6, 2, 9, 2, 6, 4, 4, 4, 7, 2, 6, 6, 6, 2, 6, 2, 6, 8

Offset

1,2

Comments

For odd numbers the intersection is empty.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A000005(2n) - A060764(2n).

Example

For n=35, 2n=70; divisors={1,2,5,7,10,14,35,70}; differences={1,3,2,3,4,21,35}; intersection={1,2,35}, so a(35)=3.

Mathematica

a[n_ ] := Length[Intersection[Drop[d=Divisors[2n], 1]-Drop[d, -1], d]]
Table[Length[Intersection[Divisors[2n], Differences[Divisors[2n]]]], {n, 110}] (* Harvey P. Dale, Nov 22 2015 *)

Prog

(PARI)
A060764(n) = { my(divs=divisors(n), diffs=vecsort(vector(#divs-1, i, divs[i+1]-divs[i]), , 8), c=#divs); for(i=1, #diffs, if(!(n%diffs[i]), c--)); (c); };
A060741(n) = (numdiv(2*n) - A060764(2*n)); \\ Antti Karttunen, Sep 21 2018

Crossrefs

Cf. A000005, A060742, A060764.

Sequence in context: A348856 A166469 A080226 * A125747 A060129 A327161

Adjacent sequences: A060738 A060739 A060740 * A060742 A060743 A060744

Keyword

nonn

Author

Labos Elemer, Apr 23 2001

Extensions

Edited by Dean Hickerson, Jan 22 2002

Status

approved