Talk:Multiplicatively perfect numbers: Difference between revisions
→To one or not to one, that is the question
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:::::: 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. --[[User:PureFox|PureFox]] ([[User talk: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. --[[User:Wherrera|Wherrera]] ([[User talk: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. --[[User:PureFox|PureFox]] ([[User talk: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. --[[User:Petelomax|Petelomax]] ([[User talk: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. --[[User:PureFox|PureFox]] ([[User talk: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. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 20:42, 9 May 2023 (UTC)
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