Talk:Descartes number

So then 198585576189 is the smallest odd spoof perfect number with one factor wrongly assumed prime? What is the smallest odd spoof perfect number with two factors wrongly assumed prime? How many factors need to be wrongly assumed prime to bring the smallest odd spoof number below a thousand? Alonso del Arte 01:01, 24 November 2010 (UTC)

To my knowledge, that's the only known (I will look again...) odd spoof perfect number (found by Descartes, which was on the quest for those elusive odd perfect numbers...) — Daniel Forgues 18:28, 24 November 2010 (UTC)

Of course the more factors that have to be wrongly assumed prime the less elegant the whole thing becomes, even though the search algorithm needs to be more sophisticated. I'll see if I can find one with two factors wrongly assumed prime. Alonso del Arte 03:29, 25 November 2010 (UTC)

Cf. A058007 Freestyle perfect numbers (perfect numbers and spoof perfect numbers) (the only odd one known is Descartes's 198585576189!) Good luck in finding a second odd spoof perfect number! The even spoof perfect numbers are aplenty, though! — Daniel Forgues 23:31, 25 November 2010 (UTC)

W.r.t. that sequence, A058007, I think it is somehow irrealistic to consider even numbers as "spoof primes", I think one should only allow odd numbers to be allowed to be taken as spoof primes (which would not exclude other even freestyle perfect numbers). — M. F. Hasler 17:33, 13 January 2013 (UTC)