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 A004214 Positive numbers that are not the sum of three nonzero squares. (Formerly M0959) 16
 1, 2, 4, 5, 7, 8, 10, 13, 15, 16, 20, 23, 25, 28, 31, 32, 37, 39, 40, 47, 52, 55, 58, 60, 63, 64, 71, 79, 80, 85, 87, 92, 95, 100, 103, 111, 112, 119, 124, 127, 128, 130, 135, 143, 148, 151, 156, 159, 160, 167, 175, 183, 188, 191, 199, 207, 208, 215, 220, 223, 231 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Not of the form x^2 + y^2 + z^2 with x, y, z >=1. Complement of A000408, but skipping the zero. - R. J. Mathar, Nov 23 2006 A025427(a(n)) = 0. - Reinhard Zumkeller, Feb 26 2015 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 David S. Bettes, Letter to N. J. A. Sloane, Nov 05 1976 EXAMPLE The smallest numbers that are the sums of 3 nonzero squares are 3=1+1+1, 6=1+1+4, 9=1+4+4, etc. MAPLE gf := sum(sum(sum(q^(x^2+y^2+z^2), x=1..25), y=1..25), z=1..25): s := series(gf, q, 500): for n from 1 to 500 do if coeff(s, q, n)=0 then printf(`%d, `, n) fi:od: MATHEMATICA f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]]; f[16] (* Ray Chandler, Dec 06 2006 *) PROG (PARI) isA000408(n)={ local(a, b) ; a=1; while(a^2+1

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Last modified October 14 07:06 EDT 2019. Contains 327995 sequences. (Running on oeis4.)