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

1,1

Comments

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

Links

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

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

Cf. A034699, A013929, A117180, A117182.

Sequence in context: A123531 A201522 A368040 * A328906 A194623 A373642

Adjacent sequences: A117178 A117179 A117180 * A117182 A117183 A117184

Keyword

nonn

Author

Leroy Quet, Mar 01 2006

Extensions

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

Status

approved