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Revision History for A343826 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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Numbers which are the product of two S-primes (A057948) in exactly one way.
(history; published version)

#24 by N. J. A. Sloane at Wed May 26 02:53:15 EDT 2021

STATUS

proposed

approved

#23 by Zachary DeStefano at Sat May 01 13:17:19 EDT 2021

STATUS

editing

proposed

Discussion

Mon May 10

17:30

Zachary DeStefano: Is there anything else I should try to provide with these sequences while waiting for approval?

#22 by Zachary DeStefano at Sat May 01 13:15:55 EDT 2021

FORMULA

a(n) == 1 (mod 4). - Hugo Pfoertner, May 01 2021

STATUS

proposed

editing

Discussion

Sat May 01

13:17

Zachary DeStefano: I have restored the formula in this sequence, A343827, and A343828.

#21 by Zachary DeStefano at Sat May 01 04:36:03 EDT 2021

STATUS

editing

proposed

Discussion

Sat May 01

04:37

Michel Marcus: why do you say formula is not correct ?

04:42

Zachary DeStefano: Michel, I misread it. The formula is correct. All of the terms are of the form 1 (mod 4).

04:44

David A. Corneth: Could it be determined if such factorization exists in exactly four ways? The number of ways only depends on prime signature mixed with mod 4 class of primes right?

04:46

Michel Marcus: then please restore formula

04:55

Zachary DeStefano: We should restore the formula. It is not letting me restore to before the Formula removal in edit 20. What am I missing?

05:06

Kevin Ryde: Yes the restore (such as it is) doesn't do that.  Cut and paste to edit back, remembering underscores _Hugo Pfoertner_ to link-ize name.

05:08

Kevin Ryde: I don't think Hugo would mind if you wanted instead to put something in words in a comment.

10:20

Hugo Pfoertner: No problem for me if the information is included in another comment. Also no need to cite me as author of this trivial fact.

#20 by Zachary DeStefano at Sat May 01 04:35:52 EDT 2021

FORMULA

a(n) == 1 (mod 4). - Hugo Pfoertner, May 01 2021

#19 by Zachary DeStefano at Sat May 01 04:34:06 EDT 2021

NAME

Numbers which are the product of two S-Primes primes (A057948) in exactly one way.

COMMENTS

There exist numbers which are the product of two S-Primes primes in exactly 1, 2, and 3 ways; however, it is unknown if any numbers exist which are the product of two S-Primes primes in exactly 4 ways.

#18 by Zachary DeStefano at Sat May 01 04:27:48 EDT 2021

EXAMPLE

153 is in S = {1,5,9, ... 4i+1, ...}, 153 is the product of 9 and *17 which are both S-Primes, primes, and admits no other S-Prime prime factorizations.

STATUS

proposed

editing

#17 by Michel Marcus at Sat May 01 04:08:49 EDT 2021

STATUS

editing

proposed

Discussion

Sat May 01

04:14

Zachary DeStefano: The PARI code that Michel added is much shorter than my C code and produces the same result.

#16 by Michel Marcus at Sat May 01 04:00:17 EDT 2021

PROG

(PARI) \\ uses is(n) from A057948

isok(n) = sumdiv(n, d, (d<=n/d) && is(d) && is(n/d)) == 1; \\ Michel Marcus, May 01 2021

STATUS

proposed

editing

Discussion

Sat May 01

04:08

Zachary DeStefano: The formula that was added is incorrect. Also, how should I upload the program? Should that be via the links section?

#15 by Hugo Pfoertner at Sat May 01 01:14:05 EDT 2021

STATUS

editing

proposed

Discussion

Sat May 01

02:19

Zachary DeStefano: I have a short C program for computing this sequence, A343827,  and A343828. Where and how should I include this? Should I provide it in all of them?

03:03

Kevin Ryde: Can upload the program once and link also in other sequences if desired (when at good state of readiness).

About A057949, ah I see.  I might think it also doesn't much need S={} in the example.  (Perhaps other sequences in the S family need care about numbers being in the set etc etc.)

03:49

Michel Marcus: S-Prime should be S-prime : see A057948

03:52

Michel Marcus: like Kevin (I guess), I think that example should simply be: 153 = 9*17 which are both S-primes, and admits no other S-prime factorizations.