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12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. So a(4) = 4.
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Amiram Eldar, <a href="/A117181/b117181.txt">Table of n, a(n) for n = 1..10000</a>
s[n_] := Max @@ Power @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)
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Highest prime-power dividing the n-th non-squarefree nonsquarefree positive integer.
a(n) is prime at 7, 11, ...
12, the 4th non-squarefree nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. So a(4)= 4.
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 : 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: a013929 := A013929(200) : for n from 1 to nops(a013929) do printf("%d, ", A034699(op(n, a013929))) ; od ; - _# _R. J. Mathar_, May 10 2007
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Leroy Quet , Mar 01 2006
_Leroy Quet _ Mar 01 2006