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A060741
Number of divisors of 2n which are also differences between consecutive divisors of 2n (ordered by size).
7
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 23 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved