A025416 Least sum of 4 nonzero squares in exactly n ways.

0, 4, 31, 28, 52, 82, 90, 135, 130, 162, 198, 202, 252, 234, 210, 346, 306, 322, 423, 370, 330, 418, 390, 462, 378, 490, 598, 450, 546, 618, 522, 594, 642, 682, 570, 770, 714, 690, 762, 906, 738, 630, 1030, 850, 1035, 978, 858, 954, 810, 1197, 1146, 882, 1090, 1206

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

Conjecture: The sequence never becomes monotonic increasing. - Jon Perry, Nov 03 2012

Examples

			a(2) = 31 because 31 = 1 + 1 + 4 + 25 = 4 + 9 + 9 + 9 and no others.
a(3) = 28 because 28 = 1 + 1 + 1 + 25 = 1 + 9 + 9 + 9 = 4 + 4 + 4 + 16 and no others.
a(4) = 52 because 52 = 1 + 1 + 1 + 49 = 1 + 1 + 25 + 25 = 4 + 16 + 16 + 16 = 9 + 9 + 9 + 25 and no others.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 501 terms from T. D. Noe)
• Index entries for sequences related to sums of squares

Programs

Mathematica

nn = 40; t = Select[Flatten[Table[a^2 + b^2 + c^2 + d^2, {a, nn}, {b, a}, {c, b}, {d, c}]], # <= nn^2 + 3 &]; {t1, t2} = Transpose[Sort[Tally[t]]]; u = Union[t2]; c = Complement[Range[u[[-1]]], u]; If[c == {}, last = u[[-1]], last = c[[1]] - 1]; Join[{0}, Table[t1[[Position[t2, n, 1, 1][[1, 1]]]], {n, last}]] (* T. D. Noe, Nov 02 2012 *)

Formula

{min k: A025428(k) = n}. - R. J. Mathar, Jun 15 2018

Extensions

0th term added by Jon Perry, Nov 02 2012