

A294742


Numbers that are the sum of 5 nonzero squares in exactly 8 ways.


0



91, 104, 106, 119, 122, 123, 126, 141, 143, 162, 185, 225
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OFFSET

1,1


COMMENTS

Theorem: There are no further terms. Proof (from a proof by David A. Corneth on Nov 08 2017 in A294736): The von Eitzen link states that if n > 5408 then the number of ways to write n as a sum of 5 squares is at least floor(sqrt(n  101) / 8) = 9. For n <= 5408, terms have been verified by inspection. Hence this sequence is finite and complete.


REFERENCES

E. Grosswald, Representations of Integers as Sums of Squares. SpringerVerlag, New York, 1985, p. 86, Theorem 1.


LINKS

Table of n, a(n) for n=1..12.
H. von Eitzen, in reply to user James47, What is the largest integer with only one representation as a sum of five nonzero squares? on stackexchange.com, May 2014
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476481.
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to sums of squares


MATHEMATICA

fQ[n_] := Block[{pr = PowersRepresentations[n, 5, 2]}, Length@Select[pr, #[[1]] > 0 &] == 8]; Select[Range@250, fQ] (* Robert G. Wilson v, Nov 17 2017 *)


CROSSREFS

Cf. A025429, A025357, A294675, A294736.
Sequence in context: A020223 A288453 A184034 * A224981 A261260 A161945
Adjacent sequences: A294739 A294740 A294741 * A294743 A294744 A294745


KEYWORD

nonn,fini,full


AUTHOR

Robert Price, Nov 07 2017


STATUS

approved



