# Talk:Multiplicatively perfect numbers

(Redirected from Talk:Special numbers)

Latest comment: 6 months ago by Rdm in topic To one or not to one, that is the question

I put up an example that fits the Wren code, but then noted its result is very different from the Ring result. Is there a problem with the Ring code or the definition of special?

- Assuming the definition is correct, then the Ring solution is not consistent with it. Take the case of n = 64, for example. 16 and 32 are also divisors but he hasn't included them in the product.--PureFox (talk) 20:12, 17 April 2023 (UTC)

- Incidentally, as the definition stands, I don't think '1' should be included as a 'special number' because it has no eligible divisors. However, it is a 'multiplicatively perfect number' because the product of its divisors (namely 1) is equal to 1 x 1. --PureFox (talk) 20:27, 17 April 2023 (UTC)

## Vote for deletion

Duplicate of Semiprime except misnamed, poor task description, and incomprehensible example code. Delete. --Thundergnat (talk) 22:52, 17 April 2023 (UTC)

- Hadn't noticed it before but, yes, it is effectively a duplicate of the Semiprime task, at least for this range of numbers. So I'd second the vote for deletion. --PureFox (talk) 23:17, 17 April 2023 (UTC)

- agree this is a duplicate task as currently defined. --Wherrera (talk) 01:46, 18 April 2023 (UTC)

- There are actually 4 'special numbers' under 500 which are not semi-prime, namely: 8, 27, 125 and 343. However, that's because they're cubes of primes and so it's only a trivial difference and not enough to justify a separate task. --PureFox (talk) 06:57, 18 April 2023 (UTC)

- Why's this still here... --Petelomax (talk) 11:12, 20 April 2023 (UTC)

- I don't think that Thundergnat (or any other member apart from Mike Mol himself) has the power to delete tasks since the switch to Miraheze. What we could do instead is to blank the page or leave it up (as a non-task) but change the language headers to 'level 3' headings which I think will prevent them from messing up the task statistics. Calmosoft has just requested that another of his putative tasks, Extreme primes, be deleted as that's also turned out to be a duplicate so whatever we do for this we can do for that as well. --PureFox (talk) 17:38, 23 April 2023 (UTC)

- Well, the language stats are already messed up with Phix and Wren shown as completing more than 100% of the tasks! As there were 8 solutions to the Extreme primes exercise, I thought the most sensible solution was to leave it up (as a draft task) but add a stretch goal (q.v) to distinguish it somewhat from the duplicates. Shall we do something similar for this one? We clearly need some sort of policy on these situations as whatever warnings are put up people seem to just add their solutions anyway. --PureFox (talk) 15:55, 25 April 2023 (UTC)

- If the page is to be deleted it could be replaced with a link to the Semiprime task. --Wherrera (talk) 21:53, 25 April 2023 (UTC)

- OK, now it's been converted to a draft task (a sensible move in the circumstances) I've added a stretch goal. Not difficult but requires a little thought. --PureFox (talk) 09:42, 8 May 2023 (UTC)

## To one or not to one, that is the question

Bit of a knee-jerk undone, the task definition has changed, otherwise I have no useful opinion on the matter. --Petelomax (talk) 23:57, 8 May 2023 (UTC)

- If MPN is defined as a number n the product of whose divisors is n^2 then there's no doubt that '1' should be included since 1 = 1 x 1. However, if we take the alternative definition (a number n the product of whose proper divisors is n), then I don't think '1' should be included as it has no proper divisors.

- As this task originally stood ('special numbers'), the second definition was applied and so '1' was excluded. However, OEIS use the first definition and therefore include '1' though they try to ride both horses at once by including the alternative definition in the comments.

- Personally, I'm inclining towards including '1' (as the J example does) and so I'm going to change my solutions to reflect that. However, given the history of this task and that it's a moot point anyway, I think we should make the inclusion of '1' optional so as not to invalidate existing solutions which excluded it in good faith. I've therefore added a note to that effect in the task description. --PureFox (talk) 08:33, 9 May 2023 (UTC)

- The product of an empty list of numbers may be thought of as 1, because 1 is the multiplicative identity. --Rdm (talk) 20:42, 9 May 2023 (UTC)