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From: Math Artist on 28 Mar 2010 19:34 1,2,3,8,5,36,7,64,27,100,11,1728,13,196,225,1024,17,5832,19,8000,441,484, 23,331776,125,676,729,21952,29,810000,31,32768,1089,1156,1225,100776 96,37,1444,1521,2560000,41,... ( Pd(n) is the product of all positive divisors of n.)
From: What you are reading is Philosophy and P Versus NP. on 29 Mar 2010 22:38
On Mar 29, 5:34 am, Dan Cass <dc... (a)sjfc.edu> wrote:> > 1,2,3,8,5,36,7,64,27,100,11,1728,13,196,225,1024,17,58 > > 32,19,8000,441,484, > > 23,331776,125,676,729,21952,29,810000,31,32768,1089,11 > > 56,1225,100776 > > 96,37,1444,1521,2560000,41,... > > ( Pd(n) is the product of all positive divisors of > > n.) > > For example the divisors of 4 being 1,2,4 with product 8, > explains your fourth entry of the sequence 1,2,3,8,... > > Though I see how you construct your sequence, it seems > you only present it, with no conjectures etc. made > about it... > > Maybe you should ask if the sequence has a name, or > if there are known results about it. Dear Mr. Cass: The name as written was 'divisor products', but if there are any other names, please do tell me! All I saw was a basic beauty and simplicity worth sharing in all respects. But now that I have you engaged and you clearly a mind to visualize these sorts of things, here's a leap! Given this first set of 'Divisor Products' given (first paragraph below): 1,2,3,8,5,36,7,64,27,100,11,1728,13,196,225,1024,17,5832,19,8000,441,484, 23,331776,125,676,729,21952,29,810000,31,32768,1089,1156,1225,100776 96,37,1444,1521,2560000,41,... Is indeed it true to be the case clearly before our eyes that: ( Pd(n) is the product of all positive divisors of n.)? (and if so, then can we continue?) and write... N O P Q R S T U V W X Y Z 14 15 16 17 18 19 20 21 22 23 24 25 26 17 And then could we take this set (the first one and compare it to)?: 'Proper Divisor Products': 1,1,1,2,1,6,1,8,3,10,1,144,1,14,15,64,1,324,1,400,21,22,1,13824,5,26,27, 784,1,27000,1,1024,33,34,35,279936,1,38,39,64000,1,... ( Pd(n) is the product of all positive divisors of n but n.) I guess what I am saying is I see a way to take ten numbers and twenty- six letters and boil it down to something by which we are able to compare as two things? (Perhaps, out of my earnest, and overzealot naivie, I have rushed to judgment on the importancde of boilding down things into sets of two, but it seems to me this is especially of importance in number theory as it relates to the computer science area? Expound, amaze me, I have to admit you did when you saw what you saw without a detailed or lengthy diatribe necessary to spot it. ' Is it not promising, the design is inherent, so much so you spotted it wouth but two words! ' Thank you, Musatov |