cp's OEIS Frontend

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

%I A080654 #36 Mar 04 2016 12:37:09
%S A080654 5,20,29,62,53,80,77,91,101,107,128,133,131,139,166,163,181,187,179,
%T A080654 219,203,214,227,238,211,262,275,251,291,277,314,298,259,299,326,307,
%U A080654 399,334,374,346,347,355,373,331,411,391,430,371,445,421,394,486,379,406
%N A080654 Smallest number with exactly n representations as a sum of five positive squares or 0 if no such number exists (cf. A025429).
%C A080654 It seems as if 33 is the largest number with no such representation. 60 seems to be the largest one with exactly one representation.
%C A080654 More generally, see A080673 for the largest number with n such representations. - _M. F. Hasler_, Mar 04 2016
%H A080654 Hagen von Eitzen, <a href="/A080654/b080654.txt">Table of n, a(n) for n = 1..78107</a>
%e A080654 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.
%t A080654 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 *)
%t A080654 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 *)
%Y A080654 Cf. A080673, A025429.
%K A080654 easy,nice,nonn
%O A080654 1,1
%A A080654 _Rainer Rosenthal_, Mar 01 2003
%E A080654 More terms from _Reinhard Zumkeller_, Apr 26 2004
%E A080654 Definition adjusted to cope with otherwise undefined values and b-file extended by _Hagen von Eitzen_, Jun 05 2014