A189883 Numbers n such that the square part of n is one greater than the squarefree part of n.

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

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: A222702 A352700 A012351 * A033469 A012544 A009052

Adjacent sequences: A189880 A189881 A189882 * A189884 A189885 A189886

Keyword

nonn

Author

Antonio Roldán, Apr 29 2011

Status

approved