A025288 -id:A025288 - cp's OEIS frontend

A025285 Numbers that are the sum of 2 nonzero squares in exactly 2 ways.

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

Offset: 1

David W. Wilson

nonn

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

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

Cf. A025284, A025286, A025287, A025288, A025289, A025290, A025291, A025292, A025293, A025426.

Cf. A007692.

a025285 n = a025285_list !! (n-1)
a025285_list = filter ((== 2) . a025426) [1..]
-- Reinhard Zumkeller, Feb 26 2015

selQ[n_] := Length[ Select[ PowersRepresentations[n, 2, 2], Times @@ # != 0 &]] == 2; Select[Range[1000], selQ] (* Jean-François Alcover, Oct 03 2013 *)

is(n)=sum(k=sqrtint((n-1)\2)+1,sqrtint(n-1), issquare(n-k^2))==2 \\ Charles R Greathouse IV, May 24 2016

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

a(n) >= A007692(n) with equality only for n <= 16. - Alois P. Heinz, Mar 23 2023

A025296 Numbers that are the sum of 2 nonzero squares in 5 or more ways.

Original entry on oeis.org

5525, 8125, 8450, 9425, 10625, 11050, 12025, 12325, 13325, 14365, 14450, 15725, 16250, 17225, 17425, 18125, 18785, 18850, 19825, 21125, 21250, 22100, 22525, 23125, 23725, 24050, 24505, 24650, 25625, 25925, 26650, 26825, 27625, 28730, 28925, 29725

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A025288, A025295, A025297, A025333, A051167.

N:= 10^5: # generate all entries <=N
V:= Vector(N,datatype=integer[4]):
for a from 1 to floor(sqrt(N)) do
  for b from a do
    n:= a^2 + b^2;
    if n > N then break fi;
    V[n]:= V[n]+1
od od:
select(t -> V[t] >= 5, [$1..N]); # Robert Israel, Jun 01 2025

nn = 30000; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i}]; Flatten[Position[t, ?(# >= 5 &)]] (* _T. D. Noe, Apr 07 2011 *)

cp's OEIS Frontend

A025285 Numbers that are the sum of 2 nonzero squares in exactly 2 ways.

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