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A024508
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Numbers that are a sum of 2 distinct nonzero squares in more than one way.
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8
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65, 85, 125, 130, 145, 170, 185, 205, 221, 250, 260, 265, 290, 305, 325, 340, 365, 370, 377, 410, 425, 442, 445, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 580, 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
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OFFSET
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1,1
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COMMENTS
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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
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
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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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