

A121571


Largest number that is not the sum of nth powers of distinct primes.


7




OFFSET

1,1


COMMENTS

As stated by Sierpinski, H. E. Richert proved a(1) = 6. Dressler et al. prove a(2) = 17163.
Fuller & Nichols prove T. D. Noe's conjecture that a(3) = 1866000. They also prove that 483370 positive numbers cannot be written as the sum of cubes of distinct primes.  Robert Nichols, Sep 08 2017
Noe conjectures that a(4) = 340250525752 and that 31332338304 positive numbers cannot be written as the sum of fourth powers of distinct primes.  Charles R Greathouse IV, Nov 04 2017


REFERENCES

W. Sierpinski, Elementary Theory of Numbers, Warsaw, 1964, p. 143144.


LINKS



FORMULA



EXAMPLE

a(1) = 6 because only the numbers 1, 4 and 6 are not the sum of distinct primes.


CROSSREFS

Cf. A231407 (numbers that are not the sum of distinct primes).
Cf. A121518 (numbers that are not the sum of squares of distinct primes).
Cf. A213519 (numbers that are the sum of cubes of distinct primes).
Cf. A001661 (integers instead of primes).


KEYWORD

nonn,hard,more,bref


AUTHOR



STATUS

approved



