[seqfan] Re: Numbers that are the sum of x nonzero y-th powers

Marc LeBrun mlb at well.com
Mon Aug 3 20:08:51 CEST 2020

Please take care regarding applying the wording "Numbers that are the sum of x nonzero y-th powers" -- "nonzero" isn't of course the same as "positive". 

Specifically, for odd y they are different sequences -- the nonzeros are a superset of the positives.

For example 7 is the sum of two nonzero 3rd powers (namely the cubes of -1 and 2).

A003325 2,9,16,... discussed previously in this thread doesn't include 7, and is correctly named "Numbers that are the sum of 2 positive cubes" in the OEIS entry.

In contrast there's A020894 0,2,7,9,16,... which is (also correctly) styled "Nonnegative numbers that are sums of two nonzero cubes"

(A020894 also has clarifying Examples, which are always good -- thanks Michael B. Porter!)

More information about the SeqFan mailing list