A085393 Difference between the largest and the smallest prime factor of the greatest proper divisor of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 5, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 4, 0, 9, 2, 0, 0, 1, 0, 0, 0, 11, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 4, 0, 0, 8, 0, 15, 0, 2, 0, 1, 0, 0, 0, 17, 0, 10, 0, 3, 0, 0, 0, 5, 0, 0, 0, 9, 0, 2, 0, 21, 0, 0, 0, 1, 0, 0, 8, 3, 0, 14

Offset: 1

Author

Robert G. Wilson v and Reinhard Zumkeller, Jun 26 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A014673, A085392.

Programs

Mathematica

PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; f[n_] := Block[{gpd = Divisors[n][[ -2]]}, If[gpd == 1, 0, PrimeFactors[gpd][[ -1]] - PrimeFactors[gpd][[1]] ]]; Table[ If[n == 1, 0, f[n]], {n, 1, 102}]
{1}~Join~Array[#[[-1, 1]] - #[[1, 1]] &@ FactorInteger@ Last@ Most@ Divisors@ # &, 101, 2] (* Michael De Vlieger, Dec 03 2017 *)

Formula

a(n) = A085392(n) - A014673(n).