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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A080673, A025429.

Sequence in context: A088973 A005240 A147374 * A162690 A074219 A178612

Adjacent sequences: A080651 A080652 A080653 * A080655 A080656 A080657

Keyword

easy,nice,nonn

Author

Rainer Rosenthal, Mar 01 2003

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

Status

approved