The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A189883

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A189883

Numbers n such that the square part of n is one greater than the squarefree part of n.
(history; published version)

#16 by Alois P. Heinz at Fri Nov 14 11:12:31 EST 2014

STATUS

editing

approved

#15 by Alois P. Heinz at Fri Nov 14 11:12:27 EST 2014

LINKS

Alois P. Heinz, <a href="/A189883/b189883.txt">Table of n, a(n) for n = 1..1000</a>

#14 by Alois P. Heinz at Fri Nov 14 11:09:15 EST 2014

FORMULA

a(n) = x^2 (x^2-1), where x = A067874(n). - _T. D. Noe, _, Apr 29 2011

MAPLE

for k from b(n-1)+1 while 1<>mul (i[2], i=ifactors (k^2-1)[2])

seq (a(n), n=1..50); # _Alois P. Heinz, _, Apr 29 2011

STATUS

approved

editing

#13 by Charles R Greathouse IV at Sun Aug 03 14:01:30 EDT 2014

MATHEMATICA

okQ[n_] := Module[{p, e, sfp}, {p, e} = Transpose[FactorInteger[n]]; e = Mod[e, 2]; sfp = Times @@ (p^e); n/sfp - sfp == 1]; Select[Range[10^5], okQ] (* _T. D. Noe, _, Apr 29 2011 *)

Discussion

Sun Aug 03

14:01

OEIS Server: https://oeis.org/edit/global/2267

#12 by Charles R Greathouse IV at Mon May 13 01:49:34 EDT 2013

PROG

(PARI) for(n=1, 1e3, if(issquarefree(n^2-1), print1(n^4-n^2", "))) \\ _Charles R Greathouse IV, _, Apr 29, 2011

Discussion

Mon May 13

01:49

OEIS Server: https://oeis.org/edit/global/1914

#11 by Russ Cox at Sat Mar 31 10:25:48 EDT 2012

AUTHOR

_Antonio Roldán (aroldanmart(AT)gmail.com), _, Apr 29 2011

Discussion

Sat Mar 31

10:25

OEIS Server: https://oeis.org/edit/global/487

#10 by T. D. Noe at Sat Apr 30 20:53:06 EDT 2011

STATUS

proposed

approved

#9 by Alois P. Heinz at Fri Apr 29 15:12:24 EDT 2011

MAPLE

b:= proc() 1 end:

a:= proc(n) option remember; local i, k;

if n>1 then a(n-1) fi;

for k from b(n-1)+1 while 1<>mul (i[2], i=ifactors (k^2-1)[2])

do od; b(n):=k; k^4-k^2

end:

seq (a(n), n=1..50); # Alois P. Heinz, Apr 29 2011

Discussion

Fri Apr 29

15:21

Alois P. Heinz: @Charles: It is more like a(n) ~ kn^4, with k=92.xxx; a(50000)=576634804094568223692.

#8 by T. D. Noe at Fri Apr 29 14:52:12 EDT 2011

COMMENTS

The complementary sequence, squarefree part of n is one greater than the square part of n, is A069187.

#7 by Charles R Greathouse IV at Fri Apr 29 14:50:07 EDT 2011

PROG

(PARI) for(n=1, 1e3, if(issquarefree(n^2-1), print1(n^4-n^2", "))) \\ Charles R Greathouse IV, Apr 29, 2011

Discussion

Fri Apr 29

14:53

Charles R Greathouse IV: Very nice.  Can anyone prove that a(n) ~ kn^2 as would be expected?  That would give an asymptotic formula here and at A067874.