A060763 Number of distinct differences between consecutive divisors (ordered by increasing magnitude) of n which are not also divisors of n.

0, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 3, 1, 1, 0, 2, 1, 3, 1, 1, 1, 1, 0, 3, 1, 3, 0, 1, 1, 3, 1, 1, 0, 1, 1, 4, 1, 1, 0, 2, 2, 3, 1, 1, 0, 3, 2, 3, 1, 1, 0, 1, 1, 4, 0, 3, 1, 1, 1, 3, 3, 1, 0, 1, 1, 3, 1, 3, 1, 1, 2, 4, 1, 1, 1, 3, 1, 3, 1, 1, 1, 2, 1, 3, 1, 3, 0, 1, 2, 4, 0, 1, 1, 1, 1, 5

Offset: 1

Author

Labos Elemer, Apr 24 2001

Keywords

• nonn

Examples

			For n=70, divisors={1,2,5,7,10,14,35,70}; differences={1,3,2,3,4,21,35}; the differences {3,4,21} are not divisors, so a(70)=3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060682, A060738, A060764.

Programs

Maple

f:= proc(n) local D,L;
  D:= numtheory:-divisors(n);
  L:= sort(convert(D,list));
  nops(convert(L[2..-1]-L[1..-2],set) minus D);
end proc:
map(f, [$1..200]); # Robert Israel, Jul 03 2017

Mathematica

a[n_] := Length[Complement[Drop[d=Divisors[n], 1]-Drop[d, -1], d]]

PARI

a(n) = my(d=divisors(n)); #select(x->(setsearch(d, x)==0), vecsort(vector(#d-1, k, d[k+1] - d[k]),,8)); \\ Michel Marcus, Jul 04 2017

Extensions

Edited by Dean Hickerson, Jan 22 2002