A330938 Numbers that cannot be written as the sum of four proper powers. A proper power is an integer of the form a^b where a,b are integers greater than or equal to 2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 22, 23, 27

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

Paul Pollack & Enrique Treviño, Sums of Proper Powers, The American Mathematical Monthly, 128 (2021), no. 1, p. 40.

A. Schinzel and W. Sierpinski, Sur les puissances propres, Bull. Soc. Roy. Sci. Liege, 34 (1965), pp. 550-554.

Links

Table of n, a(n) for n=1..21.

Example

The first few 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 * A347527 A022766 A249611

Adjacent sequences: A330935 A330936 A330937 * A330939 A330940 A330941

Keyword

nonn,fini,full

Author

Enrique Treviño, Jan 03 2020

Status

approved