The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A004613 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A004613

Numbers that are divisible only by primes congruent to 1 mod 4.
(history; published version)

#69 by N. J. A. Sloane at Sun Mar 24 12:48:37 EDT 2024

STATUS

proposed

approved

#68 by Michel Marcus at Thu Feb 29 11:45:38 EST 2024

STATUS

editing

proposed

Discussion

Sun Mar 24

00:32

Robert Munafo: Is there a reference to the explanation or proof that the new octagon-related comment is equivalent to the sequence definition and/or one of the other established equivalences?

03:31

Robert Munafo: I see what is probably some relevant discussion in the draft edits of A370082.

#67 by Michel Marcus at Thu Feb 29 11:45:10 EST 2024

COMMENTS

Also 1/7 of the area of the n-th largest octagon with angles 3*Pi/4, along the perimeter of which there are only 8 nodes of the square lattice - at its vertices. - _Alexander M. Domashenko_, Feb 21 2024

perimeter of which there are only 8 nodes of the square lattice - at its

vertices. - Alexander M. Domashenko, Feb 21 2024

STATUS

proposed

editing

#66 by Alexander M. Domashenko at Thu Feb 29 03:25:56 EST 2024

STATUS

editing

proposed

#65 by Joerg Arndt at Wed Feb 21 06:54:40 EST 2024

COMMENTS

Numbers k such that there is a "knight's move" of Euclidean distance sqrt(k) which allows the whole of the 2D lattice to be reached. For example, a knight which travels 4 units in any direction and then 1 unit at right angles to the first direction moves a distance sqrt(17) for each move. This knight can reach every square of an infinite chessboard. Also 1/7 of the area of the n-th largest octagon with angles 3*Pi/4, along the

Also 1/7 of the area of the n-th largest octagon with angles 3*Pi/4, along the

vertices. -_ _Alexander M. Domashenko_, Feb 21 2024

STATUS

proposed

editing

Discussion

Wed Feb 28

07:30

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A004613 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Thu Feb 29

03:25

Alexander M. Domashenko: Colleagues. On February 21, I added my own comment. I propose to discuss it.

#64 by Alexander M. Domashenko at Wed Feb 21 06:34:09 EST 2024

STATUS

editing

proposed

#63 by Alexander M. Domashenko at Wed Feb 21 06:29:35 EST 2024

COMMENTS

1/7 perimeter of the area which there are only 8 nodes of the nsquare lattice -th largest octagon with angles 3*Pi/4, along the at its

perimeter of which there are only 8 nodes of the square lattice - at its

vertices.-Alexander M. Domashenko, Feb 21 2024

Discussion

Wed Feb 21

06:34

Alexander M. Domashenko: Added author's comment.

#62 by Alexander M. Domashenko at Wed Feb 21 06:25:57 EST 2024

COMMENTS

1/7 of the area of the n-th largest octagon with angles 3*Pi/4, along the

perimeter of which there are only 8 nodes of the square lattice - at its

vertices.-Alexander M. Domashenko, Feb 21 2024

STATUS

approved

editing

#61 by Joerg Arndt at Wed Feb 21 06:10:07 EST 2024

COMMENTS

Also gives solutions z to x^2+y^2=z^4 with gcd(x,y,z)=1 and x,y,z positive. - John Sillcox (johnsillcox(AT)hotmail.com), Feb 20 2004A065338(a(n)) = 1. - Reinhard Zumkeller, Jul 10 2010Product_{k=1..A001221(a(n))} A079260(A027748(a(n),k)) = 1. - Reinhard Zumkeller, Jan 07 2013A062327(a(n)) = A000005(a(n))^2. (These are the only numbers that satisfy this equation.) - Benedikt Otten, May 22 2013Numbers that are positive integer divisors of 1 + 4*x^2 where x is a positive integer. - Michael Somos, Jul 26 2013

Also gives solutions z to x^2+y^2=z^4 with gcd(x,y,z)=1 and x,y,z positive. - John Sillcox (johnsillcox(AT)hotmail.com), Feb 20 2004

A065338(a(n)) = 1. - Reinhard Zumkeller, Jul 10 2010

Product_{k=1..A001221(a(n))} A079260(A027748(a(n),k)) = 1. - Reinhard Zumkeller, Jan 07 2013

A062327(a(n)) = A000005(a(n))^2. (These are the only numbers that satisfy this equation.) - Benedikt Otten, May 22 2013

Numbers that are positive integer divisors of 1 + 4*x^2 where x is a positive integer. - Michael Somos, Jul 26 2013

Also 1/7 of the area of the n-th largest octagon with

angles 3*Pi/4, along the perimeter of which there are only 8 nodes of the

square lattice - at its vertices.-Alexander M. Domashenko, Feb 12 2024

KEYWORD

nonn,nice,easy,changed

STATUS

proposed

approved

#60 by Alexander M. Domashenko at Wed Feb 21 05:16:46 EST 2024

STATUS

editing

proposed