OFFSET
2,2
COMMENTS
(n-1)/(d(n)-1) is an integer if and only if n is in sequence A096738.
EXAMPLE
The positive divisors of 12 are 1,2,3,4,6,12. The differences between the pairs of consecutive divisors are 2-1=1, 3-2=1, 4-3=1, 6-4=2, 12-6=6. The average of these differences is (1+1+1+2+6)/5 = 11/5. So a(12) = floor(11/5) = 2.
MAPLE
A131755 := proc(n) local dvs ; dvs := sort(convert(numtheory[divisors](n), list)) ; floor(add(op(i, dvs)-op(i-1, dvs), i=2..nops(dvs))/(nops(dvs)-1)) ; end: seq(A131755(n), n=2..80) ; # R. J. Mathar, Oct 24 2007
MATHEMATICA
Floor/@(Mean[Differences[Divisors[#]]]&/@Range[2, 80]) (* Harvey P. Dale, Dec 13 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Sep 17 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 24 2007
STATUS
approved