[seqfan] Re: nonpowers in A001481

Jonathan Post jvospost3 at gmail.com
Sat Jan 15 18:56:48 CET 2011

```I like to look for primes in functions created by adding, as that

That is, look at
A001222(a(n)) = primes counted, with multiplicity, of numbers that are
the sum of two nonnegative squares.  (but why is nonnegative needed,
as it is for cubes?).  Your saying not perfect powers is then
equivalent to saying that the sum of two squares is not in A001597.

2 is prime
5 is prime
10 = 2 x 5
13 is prime
17 is prime
18 = 2 x 3^2
20 = 2^2 x 5
26 = 2 x 13
29 is prime
34 = 2 x 17
37 is prime
40 = 2^3 x 5
41 is prime
45 = 3^2 x 5
50 = 2 x 5^2
52 = 2^2 x 13
53 is prime
58 = 2 x 29
61 is prime
65 = 5 x 13
68 = 2^2 x 17

On Sat, Jan 15, 2011 at 9:33 AM, Joerg Arndt <arndt at jjj.de> wrote:
> I am tempted to submit a sequence as follows:
> "Numbers that are the sum of 2 nonnegative squares
>  and not perfect powers."
>
> 2, 5, 10, 13, 17, 18, 20, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, ...
>
> Does that seem to be a good idea?
>
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```