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 A180968 The only integers that cannot be partitioned into a sum of six positive squares. 2
 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 16, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From R. J. Mathar, Sep 11 2012: (Start) Not the sum of 7 positive squares: 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 17, 20. Not the sum of 8 positive squares: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 18, 21. Not the sum of 9 positive squares: 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 19, 22. Not the sum of 10 positive squares: 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 20, 23. (End) REFERENCES Dubouis, E.; L'Interm. des math., vol. 18, (1911), pp. 55-56, 224-225. Grosswald, E.; Representation of Integers as Sums of Squares, Springer-Verlag, New York Inc., (1985), pp.73-74. LINKS Gordon Pall, On Sums of Squares, The American Mathematical Monthly, Vol. 40, No. 1, (January 1933), pp. 10-18. FORMULA Let B be the set of integers {1,2,4,5,7,10,13}. Then, for s>=6, every integer can be partitioned into a sum of s positive squares except for 1,2,...,s-1 and s+b where b is a member of the set B [Dubouis]. EXAMPLE As the sixth integer which cannot be partitioned into a sum of six positive squares is 7, we have a(6)=7. MATHEMATICA s=6; B={1, 2, 4, 5, 7, 10, 13}; Union[Range[s-1], s+B]//Sort CROSSREFS Cf. A047701 (not the sum of 5 squares) Sequence in context: A025199 A213858 A277992 * A191847 A321290 A274337 Adjacent sequences:  A180965 A180966 A180967 * A180969 A180970 A180971 KEYWORD fini,full,nonn AUTHOR Ant King, Sep 30 2010 STATUS approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)