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A117182 a(n) = A117181(n) - A117180(n).

%I A117182 #18 Feb 11 2021 03:56:58
%S A117182 0,0,0,1,0,7,1,5,0,0,3,0,5,3,7,4,13,0,23,9,25,1,2,2,0,13,1,22,15,11,0,
%T A117182 4,3,7,19,29,47,2,21,5,23,9,25,4,5,0,27,0,7,0,8,22,9,3,7,46,33,23,11,
%U A117182 8,10,27,79,37,5,0,10,39,18,5,5,15,43,20,61,45,9,17,14,14,3,49,19,7,25,16,16
%N A117182 a(n) = A117181(n) - A117180(n).
%H A117182 Amiram Eldar, <a href="/A117182/b117182.txt">Table of n, a(n) for n = 1..10000</a>
%e A117182 12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. 3 is the smallest prime power dividing 12. So a(4) = 4 - 3 = 1.
%p A117182 A013929 := proc(nmax) local a,n ; a := [] ; n :=1 ; while nops(a) < nmax do if not numtheory[issqrfree](n) then a := [op(a),n] ; fi ; n := n+1 ; od ; a ; end :
%p A117182 A034699 := proc(n) local ifs,res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1,op(i,ifs))^op(2,op(i,ifs)), i=1..nops(ifs)) ; max(%) ; fi ; end:
%p A117182 A034684 := proc(n) local ifs,res; if n = 1 then 1 ; else ifs := ifactors(n)[2] ; seq(op(1,op(i,ifs))^op(2,op(i,ifs)), i=1..nops(ifs)) ; min(%) ; fi ; end:
%p A117182 a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ",A034699(op(n,a013929))-A034684(op(n,a013929))) ; od ; # _R. J. Mathar_, May 10 2007
%t A117182 s[n_] := Differences[MinMax[Power @@@ FactorInteger[n]]][[1]]; s /@ Select[Range[250], !SquareFreeQ[#] &] (* _Amiram Eldar_, Feb 11 2021 *)
%Y A117182 Cf. A117180, A117181.
%K A117182 nonn
%O A117182 1,6
%A A117182 _Leroy Quet_, Mar 01 2006
%E A117182 More terms from _R. J. Mathar_, May 10 2007