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 A060682 Number of distinct differences between consecutive divisors of n (ordered by size). 15
 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 3, 1, 4, 3, 3, 1, 4, 2, 3, 3, 5, 1, 5, 1, 5, 3, 3, 3, 5, 1, 3, 3, 5, 1, 4, 1, 5, 4, 3, 1, 5, 2, 5, 3, 5, 1, 4, 3, 6, 3, 3, 1, 7, 1, 3, 4, 6, 3, 5, 1, 5, 3, 6, 1, 6, 1, 3, 3, 5, 3, 5, 1, 7, 4, 3, 1, 6, 3, 3, 3, 7, 1, 7, 2, 5, 3, 3, 3, 6, 1, 5, 4, 6, 1, 5, 1, 7, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Number of all differences for n is d(n)-1 = A000005(n)-1. Increments are not necessarily different, so a(n)<=d(n)-1. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 2..10000 A. Balog, P. ErdÅ‘s and G. Tenenbaum, On Arithmetic Functions Involving Consecutive Divisors, In: Analytical Number Theory, pp. 77-90, Birkhauser, Basel, 1990. Jason Earls, Smarandache iterations of the first kind on functions involving divisors and prime factors, in Smarandache Notions Journal (2004), Vol. 14.1, page 264. EXAMPLE For n=70, divisors={1,2,5,7,10,14,35,70}; differences={1,3,2,3,4,21,35}; a(70) = number of distinct differences = 6. MATHEMATICA a[n_ ] := Length[Union[Drop[d=Divisors[n], 1]-Drop[d, -1]]] PROG (Haskell) import Data.List (nub, genericLength) a060682 = genericLength . nub . a193829_row -- Reinhard Zumkeller, Jun 25 2015 (PARI) a(n) = my(d=divisors(n)); #vecsort(vector(#d-1, k, d[k+1] - d[k]), , 8); \\ Michel Marcus, Jul 04 2017 CROSSREFS Cf. A000005, A060680, A060681, A060683. Cf. A193829. Sequence in context: A173442 A112309 A160006 * A280363 A217743 A238845 Adjacent sequences:  A060679 A060680 A060681 * A060683 A060684 A060685 KEYWORD nonn AUTHOR Labos Elemer, Apr 19 2001 EXTENSIONS Edited by Dean Hickerson, Jan 22 2002 STATUS approved

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Last modified March 29 14:58 EDT 2020. Contains 333107 sequences. (Running on oeis4.)