Talk:Highly cototient number

The article says:

"While 1 is the smallest odd highly totient number, it is not the only odd highly cototient number."

This implies 1 is a highly cototient number, while the definition at the start of the page, and the sequence given don't include 1. Secondly, even if it were, the presence of the sequence makes it quite clear it is not the only odd higly cototient number.

I propose removing this sentence from the article.

Also, does the author know if all the highly cototient numbers larger than 167 are congruent to 9 (modulo 10), or is that (a) just an oddity of the first few items on the list, (b) an unproven hypothesis?

146.232.75.208 11:03, 18 September 2006 (UTC)[reply]

I've reworded the sentence, hopefully it's clearer now. The thing about 1 is that it is so extremely highly cototient, it's off the meter. It is obvious that phi(p) = p - 1, therefore p - phi(p) = 1, and since primes are infinite, so is 1 a cototient answer infinitely many times.

I am one of the persons who has edited this article in the past, so I will assume your question to the "author" addresses me. The answer to that question is (b) an unproven hypothesis. Here are a few more values beyond the ones listed in Sloane's OEIS:

7979,8189,9029,9239

These have not been independently verified yet, however. The further out you go, the more numbers you have to factor and the more processor-intensive the search becomes. A theoretical breakthrough is necessary if this hypothesis is to be proven or disproven. Anton Mravcek 15:19, 18 September 2006 (UTC)[reply]

What is a "Highly cototient number" ?

I am no further forward than I was before clicking on a link to get here.

I wonder if someone could write an article that could explain cototient to someone who doesn't already know what it means ?

PS the word does not appear in the Oxford English Dictionary although 'totient' does Cannonmc (talk) 00:57, 7 April 2014 (UTC)[reply]

Cototient now links to where it is defined. Bubba73 ^{You talkin' to me?} 01:31, 7 April 2014 (UTC)[reply]

I have defined it here instead in a new section Highly cototient number#Example. PrimeHunter (talk) 02:17, 7 April 2014 (UTC)[reply]