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A025285
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Numbers that are the sum of 2 nonzero squares in exactly 2 ways.
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9
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50, 65, 85, 125, 130, 145, 170, 185, 200, 205, 221, 250, 260, 265, 290, 305, 338, 340, 365, 370, 377, 410, 442, 445, 450, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 578, 580, 585, 610, 625, 629, 680, 685, 689, 697, 730, 740, 745, 754, 765, 785, 793, 800, 820
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OFFSET
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1,1
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COMMENTS
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Order and signs don't count. E.g. 50 = 5^2+5^2 = 7^2+1^2 (= (-5)^2+5^2, but that doesn't count as different).
A131574 is a subsequence. - Zak Seidov, Jan 31 2014
A025426(a(n)) = 2. - Reinhard Zumkeller, Feb 26 2015
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Square Number.
G. Xiao, Two squares
Index entries for sequences related to sums of squares
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MATHEMATICA
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selQ[n_] := Length[ Select[ PowersRepresentations[n, 2, 2], Times @@ # != 0 &]] == 2; Select[Range[1000], selQ] (* Jean-François Alcover, Oct 03 2013 *)
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PROG
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(Haskell)
a025285 n = a025285_list !! (n-1)
a025285_list = filter ((== 2) . a025426) [1..]
-- Reinhard Zumkeller, Feb 26 2015
(PARI) is(n)=sum(k=sqrtint((n-1)\2)+1, sqrtint(n-1), issquare(n-k^2))==2 \\ Charles R Greathouse IV, May 24 2016
(PARI) is(n)=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)==4 \\ Charles R Greathouse IV, May 24 2016
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CROSSREFS
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Cf. A025284, A025286, A025287, A025288, A025289, A025290, A025291, A025292, A025293, A025426.
Sequence in context: A109552 A206263 A007692 * A092541 A335233 A180103
Adjacent sequences: A025282 A025283 A025284 * A025286 A025287 A025288
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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