A135280 - OEIS

%I #13 Sep 18 2015 03:46:49

%S 4,10,20,25,34,50,52,74,85,100,130,164,170,185,202,244,250,260,289,

%T 290,325,340,370,394,410,442,452,500,505,514,580,610,629,650,676,724,

%U 725,802,820,850,884,962,970,985,1010,1060,1105,1130,1154,1220,1252,1285

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

%H Charles R Greathouse IV, <a href="/A135280/b135280.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p 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

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

%o (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

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

%K easy,nonn

%O 1,1

%A _Masahiko Shin_, Dec 02 2007

%E Corrected and extended by _Stefan Steinerberger_ and _R. J. Mathar_, Dec 05 2007