A135280 Numbers n of the form n = (x^2+1)(y^2+1), x,y > 0.

4, 10, 20, 25, 34, 50, 52, 74, 85, 100, 130, 164, 170, 185, 202, 244, 250, 260, 289, 290, 325, 340, 370, 394, 410, 442, 452, 500, 505, 514, 580, 610, 629, 650, 676, 724, 725, 802, 820, 850, 884, 962, 970, 985, 1010, 1060, 1105, 1130, 1154, 1220, 1252, 1285

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

The associated (x^2,y^2)-tuples are (1,1), (1,4), (1,9), (4,4), (1,16), (4,9), (1,25), (1,36), (4,16), (1,49) etc., producing 2*2=4, 2*5=10, 2*10=20, 5*5=25 etc.

Maple

isA135280 := proc(n) local d ; for d in numtheory[divisors](n) do if d > 1 and n/d > 1 then if issqr(d-1) and issqr(n/d-1) then RETURN(true) ; fi ; fi ; od: RETURN(false) ; end: for n from 4 to 800 do if isA135280(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Dec 12 2007

Mathematica

Take[Union[(#[[1]]^2+1)(#[[2]]^2+1)&/@Tuples[Range[30], 2]], 60] (* Harvey P. Dale, Feb 15 2012 *)

Prog

(PARI) list(lim)=my(v=List(), t, X); for(x=1, sqrtint(lim\2-1), X=x^2+1; for(y=1, min(sqrtint(lim\X-1), x), listput(v, X*y^2+X))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Oct 27 2013

Crossrefs

Cf. A002808, which has form (x+1)(y+1), x, y > 0.

Sequence in context: A086176 A015789 A145021 * A100436 A348011 A009882

Adjacent sequences: A135277 A135278 A135279 * A135281 A135282 A135283

Keyword

easy,nonn

Author

Masahiko Shin, Dec 02 2007

Extensions

Corrected and extended by Stefan Steinerberger and R. J. Mathar, Dec 05 2007

Status

approved