A004433
Numbers that are the sum of 4 distinct nonzero squares: of form w^2+x^2+y^2+z^2 with 0
30, 39, 46, 50, 51, 54, 57, 62, 63, 65, 66, 70, 71, 74, 75, 78, 79, 81, 84, 85, 86, 87, 90, 91, 93, 94, 95, 98, 99, 102, 105, 106, 107, 109, 110, 111, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 129, 130, 131, 133, 134, 135, 137
Offset: 1
Examples
30 = 1^2+2^2+3^2+4^2.
Links
Crossrefs
Programs
-
Haskell
a004433 n = a004433_list !! (n-1) a004433_list = filter (p 4 $ tail a000290_list) [1..] where p k (q:qs) m = k == 0 && m == 0 || q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m) -- Reinhard Zumkeller, Apr 22 2013 -
Mathematica
data = Flatten[ DeleteCases[ FindInstance[ w^2 + x^2 + y^2 + z^2 == # && 0 < w < x < y < z < #, {w, x, y, z}, Integers] & /@ Range[137], {}], 1]; w^2 + x^2 + y^2 + z^2 /. data (* Ant King, Oct 17 2010 *) Select[Union[Total[#^2]&/@Subsets[Range[10],{4}]],#<=137&] (* Harvey P. Dale, Jul 03 2011 *) -
PARI
list(lim)=my(v=List([30, 39, 46, 50, 51, 54, 57, 62, 63, 65, 66, 70, 71, 74, 75, 78, 79, 81, 84, 85, 86, 87, 90, 91, 93, 94, 95, 98, 99, 102, 105, 106, 107, 109, 110, 111, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 129, 130, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 149, 150, 151, 153, 154, 155, 156]), u=[160, 168, 172, 176, 188, 192, 208, 220, 224, 232, 240, 256, 268, 272, 288, 292, 304, 320, 328, 352, 368, 384, 388, 400, 412, 416, 432, 448, 496, 512, 528, 544, 576, 592, 608], t=1); if(lim<156, return(select(k->k<=lim, Vec(v)))); for(n=158,lim\1, if(n
Formula
a(n) = n + O(log n). - Charles R Greathouse IV, Jan 08 2025