

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
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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.
Index entries for sequences related to sums of squares


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 !! (n1)
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

N. J. A. Sloane and J. H. Conway


EXTENSIONS

More terms from Arlin Anderson (starship1(AT)gmail.com)


STATUS

approved



