A117181 Highest prime-power dividing the n-th nonsquarefree positive integer.

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

Author

Leroy Quet, Mar 01 2006

Keywords

• nonn

Comments

a(n) is prime at 7, 11, ...

Examples

			12, the 4th nonsquarefree positive integer, is 2^2 * 3. 2^2 = 4 is the largest prime power dividing 12. So a(4) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034699, A013929, A117180, A117182.

Programs

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 *)

Formula

a(n) = A034699(A013929(n)).

Extensions

More terms from R. J. Mathar, May 10 2007