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 A000413 Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)*Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives A(A000092(n)). (Formerly M4367 N1833) 5
 1, 7, 19, 57, 81, 251, 437, 691, 739, 1743, 3695, 6619, 8217, 9771, 14771, 15155, 16831, 18805, 26745, 30551, 41755, 46297, 54339, 72359, 86407, 96969, 131059, 344859, 395231, 519963, 607141, 677397, 741509, 893019, 917217, 1288415, 1406811, 1789599, 1827927, 3085785, 3216051, 3444439, 3524869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The initial value a(0) = 1 corresponds to an initial A000092(0) = 0 which is the index of a record in the sense that the value P(0) = 0 is larger than all preceding values, because there are none. - M. F. Hasler, May 04 2022 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310. FORMULA a(n) = A117609(A000092(n)), considering A000092(0) = 0. - M. F. Hasler, May 04 2022 MATHEMATICA P[n_] := (s = Sum[SquaresR[3, k], {k, 0, n}]) - Round[(4/3)*Pi*n^(3/2)]; record = 0; A000092 = Reap[For[n = 0, n <= 10^4, n++, If[(p = Abs[P[n]]) > record, record = p; Print[s]; Sow[s]]]][[2, 1]] (* Jean-François Alcover, Feb 08 2016, after M. F. Hasler in A000092 *) CROSSREFS Cf. A000323, A000036, A000092, A000099, A000223. Cf. A117609 (A(n) in name). Sequence in context: A002714 A126361 A069005 * A263335 A155335 A155226 Adjacent sequences:  A000410 A000411 A000412 * A000414 A000415 A000416 KEYWORD nonn AUTHOR EXTENSIONS Revised Jun 28 2005 a(37)-a(42) from Vincenzo Librandi, Aug 21 2016 STATUS approved

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)