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 A330938 Numbers that cannot be written as the sum of four proper powers. A proper power is an integer number m of the form a^b where a,b are integers greater than or equal to 2. 0
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 22, 23, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS There is a proof by Schinzel and Sierpinski that if n >= 33^17 + 12, then n can be written as a sum of four proper powers. Paul Pollack and Enrique Treviño improved that result to find the complete list. REFERENCES A. Schinzel and W. Sierpinski, Sur les puissances propres, Bull. Soc. Roy. Sci. Liege, 34 (1965), pp. 550-554. LINKS EXAMPLE The first missing terms are 16 = 2^2 + 2^2 + 2^2 + 2^2 20 = 2^2 + 2^2 + 2^2 + 2^3 21 = 2^2 + 2^2 + 2^2 + 3^2 24 = 2^2 + 2^2 + 2^3 + 2^3 25 = 2^2 + 2^2 + 2^3 + 3^2 26 = 2^2 + 2^2 + 3^2 + 3^2 28 = 2^2 + 2^3 + 2^3 + 2^3 CROSSREFS Cf. A001597. Sequence in context: A123093 A191932 A044920 * A022766 A249611 A323035 Adjacent sequences:  A330935 A330936 A330937 * A330939 A330940 A330941 KEYWORD nonn,fini,full AUTHOR Enrique Treviño, Jan 03 2020 STATUS approved

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Last modified June 2 09:31 EDT 2020. Contains 334769 sequences. (Running on oeis4.)