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 A000419 Numbers that are the sum of 3 but no fewer nonzero squares. 10
 3, 6, 11, 12, 14, 19, 21, 22, 24, 27, 30, 33, 35, 38, 42, 43, 44, 46, 48, 51, 54, 56, 57, 59, 62, 66, 67, 69, 70, 75, 76, 77, 78, 83, 84, 86, 88, 91, 93, 94, 96, 99, 102, 105, 107, 108, 110, 114, 115, 118, 120, 123, 126, 129, 131, 132, 133, 134, 138, 139, 140, 141, 142 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A002828(a(n)) = 3; A025427(a(n)) > 0. - Reinhard Zumkeller, Feb 26 2015 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 311. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Square Number. FORMULA Legendre: a nonnegative integer is a sum of three (or fewer) squares iff it is not of the form 4^k m with m == 7 (mod 8). MATHEMATICA Select[Range[150], SquaresR[3, #]>0&&SquaresR[2, #]==0&] (* Harvey P. Dale, Nov 01 2011 *) PROG (Haskell) a000419 n = a000419_list !! (n-1) a000419_list = filter ((== 3) . a002828) [1..] -- Reinhard Zumkeller, Feb 26 2015 (PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return( n/4^valuation(n, 4)%8 !=7 ))); 0 \\ Charles R Greathouse IV, Feb 07 2017 CROSSREFS Cf. A000378, A000408, A000415, A002828, A004215, A025427. Sequence in context: A022155 A066157 A073159 * A178890 A115821 A115767 Adjacent sequences:  A000416 A000417 A000418 * A000420 A000421 A000422 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Arlin Anderson (starship1(AT)gmail.com) STATUS approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)