tag:blogger.com,1999:blog-3722233.post2123238999140362571..comments2021-10-18T17:43:52.487-05:00Comments on Computational Complexity: An interesting SummationLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3722233.post-72760553449690552182008-10-22T04:50:00.000-05:002008-10-22T04:50:00.000-05:00By the same token, if you delet the ^n, you get th...By the same token, if you delet the ^n, you get the Kempner numbers :<BR/><A>http://www.research.att.com/~njas/sequences/A002034</A>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-1715394660411277232008-10-21T15:58:00.000-05:002008-10-21T15:58:00.000-05:00For any fixed m, the infinite sum is actually fini...For any fixed m, the infinite sum is actually finite since n divides k! for all k>=n. I have not looked at this carefully, but I think that p(n) is n minus the number of non-negative integers k less than n for which k!^n is a multiple of n.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58292127179596362062008-10-21T13:11:00.000-05:002008-10-21T13:11:00.000-05:00ignore the previous comment. I was forgetting the...ignore the previous comment. I was forgetting the "^n"<BR/><BR/>Anyone know the value with the "^n" deleted?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-61138848174776707372008-10-21T13:00:00.000-05:002008-10-21T13:00:00.000-05:00kkmd: not quite. Suppose n is a large power of 2....kkmd: not quite. Suppose n is a large power of 2.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32308417994156124022008-10-21T07:35:00.000-05:002008-10-21T07:35:00.000-05:00It seems to me p(n) is the largest prime factor of...It seems to me p(n) is the largest prime factor of n.<BR/><BR/>The sum is counting how many k's there are such that k!^n/n is not an integer, which happens iff some prime factor of n is larger than k.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-80990248210999845242008-10-20T15:50:00.000-05:002008-10-20T15:50:00.000-05:00Why don't you simply type it in, like so: π?Why don't you simply type it in, like so: π?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-20490936688606551592008-10-20T15:27:00.000-05:002008-10-20T15:27:00.000-05:00Use LaTeX to make a GIF image. For example, from h...Use LaTeX to make a GIF image. For example, from here:<BR/><BR/>http://thornahawk.unitedti.org/equationeditor/equationeditor.phpAnonymousnoreply@blogger.com