A100573 - OEIS

%I #23 Apr 14 2024 00:19:58

%S 0,0,0,0,0,1,0,0,0,3,0,1,0,5,2,0,0,1,0,3,4,9,0,1,0,11,0,5,0,1,0,0,8,

%T 15,2,1,0,17,10,3,0,1,0,9,2,21,0,1,0,3,14,11,0,1,6,5,16,27,0,1,0,29,4,

%U 0,8,1,0,15,20,2,0,1,0,35,2,17,4,1,0,3,0,39,0,1,12,41,26,9,0,1,6,21,28,45

%N Smallest difference between distinct prime divisors of n, or 0 if n is a prime power.

%H Antti Karttunen, <a href="/A100573/b100573.txt">Table of n, a(n) for n = 1..65537</a>

%e For 30 = 2*3*5, 2 and 3 are separated by only 1, so a(30) = 1.

%t <<NumberTheory`NumberTheoryFunctions` pfl[x_] :=PrimeFactorList[x] pd[x_] :=Delete[RotateLeft[pfl[x]]-pfl[x], -1] Table[Min[pd[w]], {w, 1, 1000}] (* _Labos Elemer_, Jan 05 2005 *)

%t Table[Min[Differences[Transpose[FactorInteger[n]][[1]]]],{n,100}]/.\[Infinity]->0 (* _Harvey P. Dale_, Jul 27 2015 *)

%o (PARI) A100573(n) = if(omega(n)<=1,0,my(ps=factor(n)[,1]); vecmin(vector((#ps)-1,i,ps[i+1]-ps[i]))); \\ _Antti Karttunen_, Mar 03 2018

%Y Cf. also A046665, A297173.

%K nonn

%O 1,10

%A _Leroy Quet_, Jan 02 2005

%E More terms from _Labos Elemer_, Jan 05 2005