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A295494
Smallest number with exactly n representations as a sum of six nonnegative squares.
3
0, 4, 9, 17, 20, 30, 29, 38, 36, 45, 52, 53, 54, 65, 74, 68, 83, 77, 90, 84, 86, 99, 100, 107, 101, 108, 110, 117, 129, 116, 131, 125, 126, 146, 152, 140, 134, 192, 156, 149, 161
OFFSET
0,2
COMMENTS
It appears that a(n) does not exist for n in {42, 55, 61, 74, 99, 100, 103, 125, 135, 139, 148, 152, 161, 162, 164, 168, 180, 182, 194, 196}; i.e., there is no integer whose number of representations is any of these values.
REFERENCES
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.
LINKS
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
MATHEMATICA
Table[SelectFirst[Range@ 200, Length@ PowersRepresentations[#, 6, 2] == n &] - Boole[n == 1], {n, 41}] (* Michael De Vlieger, Nov 26 2017 *)
CROSSREFS
Sequence in context: A313354 A313355 A313356 * A092464 A377389 A328271
KEYWORD
nonn
AUTHOR
Robert Price, Nov 22 2017
STATUS
approved