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%I A117180 #21 Feb 11 2021 03:56:39
%S A117180 4,8,9,3,16,2,4,3,25,27,4,32,4,5,4,5,3,49,2,4,2,7,3,7,64,4,8,3,4,5,81,
%T A117180 3,8,2,4,3,2,9,4,8,4,7,4,9,3,121,4,125,2,128,3,5,8,4,9,3,4,2,8,9,3,5,
%U A117180 2,4,3,169,9,4,7,11,4,8,4,7,3,4,2,8,3,9,13,4,8,4,7,9,3,8,2,4,3,2,243,4,5,8
%N A117180 Lowest prime-power dividing the n-th nonsquarefree positive integer.
%H A117180 Amiram Eldar, <a href="/A117180/b117180.txt">Table of n, a(n) for n = 1..10000</a>
%F A117180 a(n) = A034684(A013929(n)).
%e A117180 12, the 4th nonsquarefree positive integer, is 2^2 * 3. 3 is the smallest prime power dividing 12. So a(4) = 3.
%p A117180 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 : A034684 := proc(n) local ifs; 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: a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ",A034684(op(n,a013929))) ; od ; # _R. J. Mathar_, May 10 2007
%t A117180 s[n_] := Min @@ Power @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* _Amiram Eldar_, Feb 11 2021 *)
%Y A117180 Cf. A034684, A013929, A117181, A117182.
%K A117180 nonn
%O A117180 1,1
%A A117180 _Leroy Quet_, Mar 01 2006
%E A117180 More terms from _R. J. Mathar_, May 10 2007

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