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A189883 Numbers n such that the square part of n is one greater than the squarefree part of n. 1
12, 240, 1260, 20592, 38220, 65280, 104652, 159600, 233772, 809100, 1047552, 1335180, 1678320, 2083692, 2558400, 3109932, 7308912, 8500140, 9831360, 11313132, 12956400, 18970380, 21376752, 24005100, 26868672, 37008972, 49780080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Antonio Roldán, hojaynumeros.blogspot.com

FORMULA

n such that A008833(n) - A007913(n) = 1.

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

EXAMPLE

1260 = 2^2*3^2*5*7, square part: 2^2*3^2 = 36, squarefree part: 5*7 = 35, and 36 = 35+1.

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

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 *)

PROG

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

CROSSREFS

Sequence in context: A279610 A222702 A012351 * A033469 A012544 A009052

Adjacent sequences:  A189880 A189881 A189882 * A189884 A189885 A189886

KEYWORD

nonn

AUTHOR

Antonio Roldán, Apr 29 2011

STATUS

approved

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Last modified January 23 00:58 EST 2018. Contains 298093 sequences.