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Search: id:A000404
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| A000404 |
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Numbers that are the sum of 2 nonzero squares. |
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+0
47
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| 2, 5, 8, 10, 13, 17, 18, 20, 25, 26, 29, 32, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 136, 137, 145, 146, 148, 149, 153, 157, 160, 162, 164, 169, 170, 173, 178
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also numbers whose cubes are the sum of two nonzero squares. - Joe Namnath and Lawrence Sze.
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REFERENCES
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D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, p. 219, th. 251, 252.
Ian Stewart, "Game, Set and Math", Chapter 8, 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
G. Xiao, Two squares
Reinhard Zumkeller, Illustration for A084888 and A000404
Index entries for sequences related to sums of squares
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FORMULA
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Let n=2^t* p_1^a_1 * p_2^a_2 *...p_r^a_r * q_1^b_1 *q_2^b_2 *...a_s^b_s with t>=0, a_i>=0 for i=1..r, where p_i = 1 mod 4 for i=1..r and q_j =-1 mod 4 for j=1..s. Then n is a member iff 1) b_i=0 mod 2 for i=1..r and 2) either r>0 or t=1 mod 2.
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EXAMPLE
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25 = 3^2 + 4^2, therefore 25 is a term. Note that also 25^3 = 15625 = 44^2 + 117^2, therefore 15625 is a term.
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CROSSREFS
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Cf. A024509 (numbers with multiplicity), A025284, A018825. Also A050803, A050801, A001105, A033431, A084888.
Cf. A000578, A000290.
Sequence in context: A059556 A024509 A084889 this_sequence A025284 A140328 A000415
Adjacent sequences: A000401 A000402 A000403 this_sequence A000405 A000406 A000407
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas and J. H. Conway (conway(AT)math.princeton.edu)
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EXTENSIONS
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Edited by Ralf Stephan, Nov 15, 2004
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