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A025319
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Numbers that are the sum of 2 distinct nonzero squares in 9 or more ways.
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5
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71825, 93925, 122525, 138125, 143650, 156325, 160225, 173225, 187850, 204425, 209525, 223925, 226525, 235625, 244205, 245050, 257725, 267325, 273325, 276250, 287300, 292825, 296225, 300625, 308125, 308425, 312650, 320450, 333125, 337025
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OFFSET
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1,1
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COMMENTS
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Subsequence of A025300. But sequences A025319 and A025300 are different. 2*5^16 = 305175781250 = 36425^2 + 551225^2 = 78125^2 + 546875^2 = 119375^2 + 539375^2 = 189311^2 + 518977^2 = 228125^2 + 503125^2 = 265625^2 + 484375^2 = 301595^2 + 462835^2 = 359875^2 + 419125^2 = 390625^2 + 390625^2 (not distinct squares) is not in A025319. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025300 but not in A025319 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^16 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^16 is the smallest term in A025300 that is not in A025319. - Chai Wah Wu, Feb 27 2016
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares
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MATHEMATICA
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nn = 337025; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i - 1}]; Flatten[Position[t, _?(# >= 9 &)]] (* T. D. Noe, Apr 07 2011 *)
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CROSSREFS
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Sequence in context: A114661 A119397 A025300 * A097245 A025292 A025310
Adjacent sequences: A025316 A025317 A025318 * A025320 A025321 A025322
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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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