The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A217834 Total number of solutions to the equation x^2+k*y^2 = n with x > 0, y > 0, k > 0. (Order matters for the equation x^2+y^2 = n). 5
 0, 1, 1, 1, 3, 2, 2, 3, 3, 4, 3, 4, 6, 3, 3, 4, 7, 5, 5, 7, 6, 5, 4, 6, 8, 6, 6, 8, 9, 5, 6, 8, 9, 8, 5, 9, 11, 6, 6, 11, 12, 6, 8, 9, 12, 7, 6, 10, 11, 9, 8, 15, 12, 10, 8, 10, 13, 10, 8, 10, 15, 7, 9, 12, 16, 9, 10, 15, 12, 10, 8, 15, 18, 10, 9, 16, 12, 8, 11, 15, 17, 12, 9, 16, 19, 10, 9, 16, 18, 13, 12, 13, 14, 11, 9, 15, 21, 10, 14, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS If the equation x^2+y^2 = n has got two solutions (x, y), (y, x) then they will be counted differently. No solutions can exist for the values of k >= n. a(n) is the same as A216672(n) when n is not the sum of two positive squares. But when n is the sum of two positive squares, the ordered pairs for the equation x^2+y^2 = n count. For example, 10 = 3^2 + 1^2. 10 = 1^2 + 3^2. 10 = 2^2 + 6*1^2. 10 = 1^2 + 9*1^2. So a(10) = 4. On the other hand, for the sequence A216672, the ordered pair 3^2+1^2 and 1^2+3^2 will be counted as the same, and so A216672(10) = 3. LINKS Table of n, a(n) for n=1..100. PROG (PARI) for(n=1, 100, sol=0; for(k=1, n, for(x=1, n, if((issquare(n-k*x*x)&&n-k*x*x>0), sol++))); print1(sol", ")) /* V. Raman, Oct 16 2012 */ CROSSREFS Cf. A216503, A216504, A216505. Cf. A216672 (a variant of this sequence, when the order does not matter for the equation x^2+y^2 = n, i.e. if the equation x^2+y^2 = n has got two solutions (x, y), (y, x) then they will be counted as the same). Cf. A216672, A216673, A216674, A217840, A217956. Sequence in context: A115039 A032536 A115061 * A227877 A225867 A046822 Adjacent sequences: A217831 A217832 A217833 * A217835 A217836 A217837 KEYWORD nonn AUTHOR V. Raman, Oct 16 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 23:09 EST 2023. Contains 367526 sequences. (Running on oeis4.)