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

%I A060741 #12 Sep 23 2018 20:56:26
%S A060741 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,
%T A060741 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,
%U A060741 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
%N A060741 Number of divisors of 2n which are also differences between consecutive divisors of 2n (ordered by size).
%C A060741 For odd numbers the intersection is empty.
%H A060741 Antti Karttunen, <a href="/A060741/b060741.txt">Table of n, a(n) for n = 1..65537</a>
%F A060741 a(n) = A000005(2n) - A060764(2n).
%e A060741 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.
%t A060741 a[n_ ] := Length[Intersection[Drop[d=Divisors[2n], 1]-Drop[d, -1], d]]
%t A060741 Table[Length[Intersection[Divisors[2n],Differences[Divisors[2n]]]],{n,110}] (* _Harvey P. Dale_, Nov 22 2015 *)
%o A060741 (PARI)
%o A060741 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); };
%o A060741 A060741(n) = (numdiv(2*n) - A060764(2*n)); \\ _Antti Karttunen_, Sep 21 2018
%Y A060741 Cf. A000005, A060742, A060764.
%K A060741 nonn
%O A060741 1,2
%A A060741 _Labos Elemer_, Apr 23 2001
%E A060741 Edited by _Dean Hickerson_, Jan 22 2002