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Difference between the largest and the smallest prime factor of the greatest proper divisor of n.
3

%I #11 Dec 04 2017 08:59:09

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A085393/b085393.txt">Table of n, a(n) for n = 1..16384</a>

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

%t 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}]

%t {1}~Join~Array[#[[-1, 1]] - #[[1, 1]] &@ FactorInteger@ Last@ Most@ Divisors@ # &, 101, 2] (* _Michael De Vlieger_, Dec 03 2017 *)

%Y Cf. A014673, A085392.

%K nonn

%O 1,20

%A _Robert G. Wilson v_ and _Reinhard Zumkeller_, Jun 26 2003