A000419 - OEIS

%I #32 Mar 06 2021 12:57:09

%S 3,6,11,12,14,19,21,22,24,27,30,33,35,38,42,43,44,46,48,51,54,56,57,

%T 59,62,66,67,69,70,75,76,77,78,83,84,86,88,91,93,94,96,99,102,105,107,

%U 108,110,114,115,118,120,123,126,129,131,132,133,134,138,139,140,141,142

%N Numbers that are the sum of 3 but no fewer nonzero squares.

%C A002828(a(n)) = 3; A025427(a(n)) > 0. - _Reinhard Zumkeller_, Feb 26 2015

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 311.

%H Ray Chandler, <a href="/A000419/b000419.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number.</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F 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).

%t Select[Range[150],SquaresR[3,#]>0&&SquaresR[2,#]==0&] (* _Harvey P. Dale_, Nov 01 2011 *)

%o (Haskell)

%o a000419 n = a000419_list !! (n-1)

%o a000419_list = filter ((== 3) . a002828) [1..]

%o -- _Reinhard Zumkeller_, Feb 26 2015

%o (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

%o (Python)

%o def aupto(lim):

%o   squares = [k*k for k in range(1, int(lim**.5)+2) if k*k <= lim]

%o   sum2sqs = set(a+b for i, a in enumerate(squares) for b in squares[i:])

%o   sum3sqs = set(a+b for a in sum2sqs for b in squares)

%o   return sorted(set(range(lim+1)) & (sum3sqs - sum2sqs - set(squares)))

%o print(aupto(142)) # _Michael S. Branicky_, Mar 06 2021

%Y Cf. A000378, A000408, A000415, A002828, A004215, A025427.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_ and _J. H. Conway_

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