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A117181
Highest prime-power dividing the n-th nonsquarefree positive integer.
3
4, 8, 9, 4, 16, 9, 5, 8, 25, 27, 7, 32, 9, 8, 11, 9, 16, 49, 25, 13, 27, 8, 5, 9, 64, 17, 9, 25, 19, 16, 81, 7, 11, 9, 23, 32, 49, 11, 25, 13, 27, 16, 29, 13, 8, 121, 31, 125, 9, 128, 11, 27, 17, 7, 16, 49, 37, 25, 19, 17, 13, 32, 81, 41, 8, 169, 19, 43, 25, 16, 9, 23, 47, 27, 64, 49
OFFSET
1,1
COMMENTS
a(n) is prime at 7, 11, ...
LINKS
FORMULA
a(n) = A034699(A013929(n)).
EXAMPLE
12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. So a(4) = 4.
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 : 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
MATHEMATICA
s[n_] := Max @@ 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