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 A000419 Numbers that are the sum of 3 but no fewer nonzero squares. 11
 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 (Python) def aupto(lim):   squares = [k*k for k in range(1, int(lim**.5)+2) if k*k <= lim]   sum2sqs = set(a+b for i, a in enumerate(squares) for b in squares[i:])   sum3sqs = set(a+b for a in sum2sqs for b in squares)   return sorted(set(range(lim+1)) & (sum3sqs - sum2sqs - set(squares))) print(aupto(142)) # Michael S. Branicky, Mar 06 2021 CROSSREFS Cf. A000378, A000408, A000415, A002828, A004215, A025427. Sequence in context: A022155 A066157 A073159 * A353716 A178890 A332933 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 November 26 05:48 EST 2022. Contains 358353 sequences. (Running on oeis4.)