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A025313
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Numbers that are the sum of 2 distinct nonzero squares in 3 or more ways.
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5
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325, 425, 650, 725, 845, 850, 925, 1025, 1105, 1300, 1325, 1445, 1450, 1525, 1625, 1690, 1700, 1825, 1850, 1885, 2050, 2125, 2210, 2225, 2405, 2425, 2465, 2525, 2600, 2650, 2665, 2725, 2825, 2873, 2890, 2900, 2925, 3050, 3125, 3145, 3250, 3380, 3400
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OFFSET
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1,1
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COMMENTS
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Sequence contains no primes (A000040) and no semiprimes (A001358). - Zak Seidov, Apr 07 2011
Sequences A025294 and A025313 are different. For example 1250 is not in A025313. A025294(9) = 1250 = 35^2 + 5^2 = 31^2 + 17^2 = 25^2 + 25^2 (not distinct squares). - Vaclav Kotesovec, Feb 27 2016
Numbers in A025294 but not in A025313 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^4 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^4 = 1250 is the smallest term in A025294 that is not in A025313. - Chai Wah Wu, Feb 27 2016
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..5386
Index entries for sequences related to sums of squares
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EXAMPLE
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325 = 1^2+18^2 = 6^2+17^2 = 10^2+15^2. [Zak Seidov, Apr 07 2011]
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MATHEMATICA
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nn = 3400; 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, _?(# >= 3 &)]] (* T. D. Noe, Apr 07 2011 *)
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CROSSREFS
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Sequence in context: A000443 A097101 A025294 * A025286 A025304 A351801
Adjacent sequences: A025310 A025311 A025312 * A025314 A025315 A025316
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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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