A080654 Smallest number with exactly n representations as a sum of five positive squares or 0 if no such number exists (cf. A025429).

5, 20, 29, 62, 53, 80, 77, 91, 101, 107, 128, 133, 131, 139, 166, 163, 181, 187, 179, 219, 203, 214, 227, 238, 211, 262, 275, 251, 291, 277, 314, 298, 259, 299, 326, 307, 399, 334, 374, 346, 347, 355, 373, 331, 411, 391, 430, 371, 445, 421, 394, 486, 379, 406

Offset: 1

Author

Rainer Rosenthal, Mar 01 2003

Keywords

• easy
• nice
• nonn

Comments

It seems as if 33 is the largest number with no such representation. 60 seems to be the largest one with exactly one representation.

More generally, see A080673 for the largest number with n such representations. - M. F. Hasler, Mar 04 2016

Examples

			a(4) = 62 because there are exactly four representations as a sum of 5 squares: 62 = 1+4+4+4+49 = 1+4+16+16+25 = 4+4+4+25+25 = 4+4+9+9+36.
		

Links

• Hagen von Eitzen, Table of n, a(n) for n = 1..78107

Crossrefs

Cf. A080673, A025429.

Programs

Mathematica

f[k_] := f[k] = Length[Select[PowersRepresentations[k, 5, 2], #[[1]] > 0 &]]; a[n_] := (k = 1; While[f[k++] != n]; k-1); Array[a, 54] (* Jean-François Alcover, Apr 26 2011 *)
f[n_] := f[n] = Block[{c = Range@ Sqrt@ n^2}, Length@ IntegerPartitions[n, {5}, c]]; t = Array[f, 50000, 0]; Table[ Position[t, n, 1, 1], {n, 190}] - 1 (* Robert G. Wilson v, Jun 01 2014 *)

Extensions

More terms from Reinhard Zumkeller, Apr 26 2004

Definition adjusted to cope with otherwise undefined values and b-file extended by Hagen von Eitzen, Jun 05 2014