1,1

Also numbers whose cubes are the sum of two nonzero squares. - Joe Namnath and Lawrence Sze.

From the formula it is easy to see that if n is in this sequence, then so are all odd powers of n. [From T. D. Noe (noe(AT)sspectra.com), Jan 13 2009]

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.

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

Let n = 2^t * p_1^a_1 * p_2^a_2 *...* p_r^a_r * q_1^b_1 * q_2^b_2 *...* q_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_j=0 mod 2 for j=1..s and 2) r>0 or t=1 mod 2 (or both).

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.

nMax=1000; n2=Floor[Sqrt[nMax-1]]; Union[Flatten[Table[a^2+b^2, {a, n2}, {b, Floor[Sqrt[nMax-a^2]]}]]]

(PARI) isA000404(n)={ for( i=1, #n=factor(n)~%4, n[1, i]==3 & n[2, i]%2 & return); n & ( vecmin(n[1, ])==1 | (n[1, 1]==2 & n[2, 1]%2))} \\ M. F. Hasler, Feb 07 2009

A001481 gives another version (allowing for zero squares).

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

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com) and J. H. Conway (conway(AT)math.princeton.edu)

Edited by Ralf Stephan, Nov 15, 2004

Corrected a typo in the formula. - M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 07 2009

Fixed erroneous Mathematica program -- T. D. Noe (noe(AT)sspectra.com), Aug 07 2009