A295752 Smallest number with exactly n representations as a sum of seven nonnegative squares.

0, 4, 9, 13, 18, 21, 25, 29, 34, 36, 37, 46, 49, 50, 45, 53, 58, 54, 68, 61, 66, 74, 69, 70, 78, 77, 81, 84, 86

Offset: 0

Author

Robert Price, Nov 26 2017

Keywords

• nonn

Comments

It appears that a(n) does not exist for n in {30, 35, 45, 49, 57, 63, 67, 75, 77, 78, 82, 84, 85, 97, 100, 101, 104, 110, 112, 115, 116, 119, 123, 124, 125, 134, 136, 137, 140, 142, 143, 148, 149, 150, 151, 158, 159, 160, 162, 168, 170, 172, 174, 175, 176, 180, 183, 184, 185, 187, 188, 191, 198}; 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.

Crossrefs

Cf. A025422, A295494.