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A080654
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Smallest number with exactly n representations as a sum of five positive squares or 0 if no such number exists (cf. A025429).
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7
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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Definition adjusted to cope with otherwise undefined values and b-file extended by Hagen von Eitzen, Jun 05 2014
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STATUS
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approved
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