cp's OEIS Frontend

A024508 Numbers that are a sum of 2 distinct nonzero squares in more than one way.

%I A024508 #38 Jun 10 2016 10:44:10
%S A024508 65,85,125,130,145,170,185,205,221,250,260,265,290,305,325,340,365,
%T A024508 370,377,410,425,442,445,481,485,493,500,505,520,530,533,545,565,580,
%U A024508 585,610,625,629,650,680,685,689,697,725,730,740,745,754,765,785,793,820,845,850,865,884,890,901,905,925,949,962,965,970,985,986,1000,1010,1025,1037,1040,1060,1066,1073,1090,1105,1125
%N A024508 Numbers that are a sum of 2 distinct nonzero squares in more than one way.
%C A024508 Appears to be n such that sigma(n)==0 (mod 4) and n is expressible as a sum of 2 squares. - _Benoit Cloitre_, Apr 20 2003
%C A024508 The comment that is in above is true most of the time. However if number of odd divisors of n that is a term of this sequence is not divisible by 4, then sigma(n) cannot be divisible by 4. For example; 325, 425, 625, 650, ... See also A000443 for more related examples. - _Altug Alkan_, Jun 09 2016
%C A024508 If m is a term then (a^2 + b^2) * m is a term for a,b > 0. Hence this sequence is closed under multiplication. - _David A. Corneth_, Jun 10 2016
%H A024508 David A. Corneth, <a href="/A024508/b024508.txt">Table of n, a(n) for n = 1..10749</a>
%H A024508 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two squares</a>
%H A024508 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t A024508 lst={};q=-1;k=1;Do[Do[x=a^2;Do[y=b^2;If[x+y==n,If[n==q&&k==1,AppendTo[lst,n]];If[n!=q,q=n;k=1,k++ ]],{b,Floor[(n-x)^(1/2)],a+1,-1}],{a,Floor[n^(1/2)],1,-1}],{n,2*6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2009 *)
%o A024508 (PARI) is(n) = {my(t=0,i);t=sum(i=1,sqrtint((n-1)\2),issquare(n-i^2));t>1} \\ _David A. Corneth_, Jun 10 2016
%o A024508 (PARI) is(n)=if(n<9,return(0)); my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f[, 1], if(f[i, 1]%4==1, t*=f[i, 2]+1, if(f[i, 2]%2, return(0)))); if(t%2, t-(-1)^v, t)/2-issquare(n/2)>1 \\ _Charles R Greathouse IV_, Jun 10 2016
%Y A024508 Cf. A001481, A025303 (exactly 2 ways), A025304 (exactly 3 ways), A025305 (exactly 4 ways), A025306 (exactly 5 ways).
%K A024508 nonn
%O A024508 1,1
%A A024508 _Clark Kimberling_