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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 (list; graph; refs; listen; history; text; internal format)
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: A135615 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

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Last modified August 5 18:00 EDT 2021. Contains 346488 sequences. (Running on oeis4.)