View source for Talk:Sequence: nth number with exactly n divisors

== Handy hints ==

Handy optimization hints: Terms in position n that is a prime number are '''always''' the nth prime raised to the (n-1)th power. E.G.

      # 1  2  3  4  5  6  7  8  9  10  11
 primes 2  3  5  7 11 13 17 19 23  29  31

    Term 7  is 17^6  == 24137569. 
    Term 11 is 31^10 == 819628286980801.

and so on. 

Non prime odd terms are '''always''' a square number. --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 18:53, 11 April 2019 (UTC)

: ''All'' &nbsp; odd terms are '''always''' a square number. &nbsp; &nbsp; -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 01:02, 12 April 2019 (UTC)

:: You are 100% correct, but these were meant to be optimization hints, not statements of general fact. Sort of an either / or kind of thing. --[[User:Thundergnat|Thundergnat]] ([[User talk:Thundergnat|talk]]) 09:59, 12 April 2019 (UTC)

: That is one <strike>hel</strike> heck of some dandy hints!! &nbsp; &nbsp; -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 18:56, 11 April 2019 (UTC)

May this is a naive question: Why 2nd term of sequence is not 2 but 3.
<br>2 has exactly 2 divisors: 1 and 2 (CalmoSoft)
: 2 is the '''first''' number with exactly 2 divisors but 3 is the '''second''' such number. So, 3 is the second term of the sequence. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 13:48, 8 March 2021 (UTC)
<br>
: Thanks PureFox, now I understand it (CalmoSoft)