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 A223728 Multiplicities for A223727: primitive sums of four distinct nonzero squares. 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 5, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 4, 2, 1, 2, 3, 1, 5, 2, 2, 2, 2, 2, 4, 3, 1, 4, 1, 1, 4, 2, 2, 2, 5, 3, 1, 6, 3, 3, 1, 2, 1, 1, 4, 4, 2, 5, 1, 3, 7, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS A223728(n) has a(n) different primitive representations as sum of four distinct nonzero squares, n>=1. LINKS Table of n, a(n) for n=1..100. FORMULA a(n) = k if there are k different solutions for A223728(n) = sum(s(j)^2, j=1..4), with 0 < s(1) < s(2) < s(3) < s(4) and gcd(s(1),s(2),s(3),s(4)) = 1. EXAMPLE a(16) = 3 because A223727(16) = 78 has three s-quadruples, namely [1, 2, 3, 8], [1, 4, 5, 6] and [2, 3, 4, 7]. a(23) = 2 from A223727(23) = 90 with s-quadruples [1, 2, 6, 7] and [1, 3, 4, 8]. CROSSREFS Cf. A223727, A223726. Sequence in context: A031243 A030394 A223726 * A030596 A031277 A001165 Adjacent sequences: A223725 A223726 A223727 * A223729 A223730 A223731 KEYWORD nonn AUTHOR Wolfdieter Lang, Mar 27 2013 STATUS approved

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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)