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Revision History for A117181 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Highest prime-power dividing the n-th nonsquarefree positive integer.
(history; published version)
#17 by Bruno Berselli at Thu Feb 11 03:56:48 EST 2021
STATUS

reviewed

approved

#16 by Joerg Arndt at Thu Feb 11 03:33:21 EST 2021
STATUS

proposed

reviewed

#15 by Michel Marcus at Thu Feb 11 02:57:30 EST 2021
STATUS

editing

proposed

#14 by Michel Marcus at Thu Feb 11 02:57:26 EST 2021
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.

STATUS

proposed

editing

#13 by Amiram Eldar at Thu Feb 11 02:44:54 EST 2021
STATUS

editing

proposed

#12 by Amiram Eldar at Thu Feb 11 02:24:27 EST 2021
LINKS

Amiram Eldar, <a href="/A117181/b117181.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

s[n_] := Max @@ Power @@@ FactorInteger[n]; s /@ Select[Range[200], !SquareFreeQ[#] &] (* Amiram Eldar, Feb 11 2021 *)

STATUS

approved

editing

#11 by Jon E. Schoenfield at Sun Aug 09 15:16:51 EDT 2015
STATUS

editing

approved

#10 by Jon E. Schoenfield at Sun Aug 09 15:16:49 EDT 2015
NAME

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

COMMENTS

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

EXAMPLE

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.

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

STATUS

approved

editing

#9 by Charles R Greathouse IV at Wed Apr 09 10:13:41 EDT 2014
AUTHOR

Leroy Quet , Mar 01 2006

Discussion
Wed Apr 09
10:13
OEIS Server: https://oeis.org/edit/global/2147
#8 by N. J. A. Sloane at Wed Feb 05 20:18:18 EST 2014
AUTHOR

_Leroy Quet _ Mar 01 2006

Discussion
Wed Feb 05
20:18
OEIS Server: https://oeis.org/edit/global/2118