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A117180
Lowest prime-power dividing the n-th nonsquarefree positive integer.
3
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, 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, 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
OFFSET
1,1
LINKS
FORMULA
a(n) = A034684(A013929(n)).
EXAMPLE
12, the 4th nonsquarefree positive integer, is 2^2 * 3. 3 is the smallest prime power dividing 12. So a(4) = 3.
MAPLE
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
MATHEMATICA
s[n_] := Min @@ Power @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Mar 01 2006
EXTENSIONS
More terms from R. J. Mathar, May 10 2007
STATUS
approved