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

Author

Labos Elemer, Apr 23 2001

Keywords

• nonn

Comments

For odd numbers the intersection is empty.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000005, A060742, A060764.

Programs

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 *)

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

Formula

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

Extensions

Edited by Dean Hickerson, Jan 22 2002