# [seqfan] Re: JVP proposes comment on Richard K. Guy's Squarefree numbers congruent to 1 mod 4.

Richard Guy rkg at cpsc.ucalgary.ca
Sun Feb 20 00:02:34 CET 2011

```I've just looked up A001244, and find no mention of RKG.
The author is Neil Sloane.
And what are ``omega=2'' and ``omega = 3'' ??      R.

On Sat, 19 Feb 2011, Jonathan Post wrote:

> Author: "R. K. Guy (rkg(AT)cpsc.ucalgary.ca)"
>
> A002144  	Pythagorean primes: primes of form 4n+1.
>
> I thought it better to list omega=2 and omega = 3 as a comment, and
> not new seqs.
>
> On Sat, Feb 19, 2011 at 12:09 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
>> I don't recall being particularly associated with this.  Note
>> that 1 is a squarefree number.
>>
>> Primes congruent to 1 mod 4 must already be a sequence in OEIS.
>> Too lazy to look it up.    R.
>>
>> On Sat, 19 Feb 2011, Jonathan Post wrote:
>>
>>> http://oeis.org/draft/A039955
>>>
>>> NAME
>>> Squarefree numbers congruent to 1 mod 4.
>>>
>>>        DATA
>>> 5, 13, 17, 21, 29, 33, 37, 41, 53, 57, 61, 65, 69, 73, 77, 85, 89, 93,
>>> 97, 101, 105, 109, 113, 129, 133, 137, 141, 145, 149, 157, 161, 165,
>>> 173, 177, 181, 185, 193, 197, 201, 205, 209, 213, 217, 221, 229, 233,
>>> 237, 241, 249, 253, 257, 265, 269
>>>
>>>        OFFSET
>>> 0,1
>>>
>>>
>>> The subsequence of primes begins: 5, 13, 17, 29, 37, 41, 53, 61, 73,
>>> 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233,
>>> 241, 257, 269.
>>>
>>> The subsequence of semiprimes begins: 21, 33, 57, 65, 69, 77, 85, 93,
>>> 133, 133, 141, 145, 161, 177, 185, 201, 205, 209, 213, 217, 221, 237,
>>> 249, 253, 265.
>>>
>>> The subsequence with more than two prime factors begins: 105 = 3 * 5 *
>>> 7, 165 = 3 * 5 * 11 [Jonathan Vos Post, Feb 19, 2011].
>>>
>>>        REFERENCES
>>> R. A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.
>>>
>>>        MATHEMATICA
>>> Select[ Select[ Range[ 2, 300 ], Max[ Transpose[ FactorInteger[ # ] ][
>>> [ 2 ] ] ]==1& ], Mod[ #, 4 ]==1& ]
>>>
>>>        CROSSREFS
>>> Cf. A039956, A039957.
>>>
>>>        KEYWORD
>>> nonn,easy,nice,changed
>>>
>>>        AUTHOR
>>> R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
>>>
>>>        STATUS
>>> proposed
```