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A060763
Number of distinct differences between consecutive divisors (ordered by increasing magnitude) of n which are not also divisors of n.
9
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
1,9
LINKS
EXAMPLE
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.
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]]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 24 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved