20200828, 14:46  #1 
Mar 2018
17×31 Posts 
numbers of yet another particular type
Consider numbers N squarefree that is in the factorisation of N there is no prime facor raised to a power greater than 1.
56238 is square free 56238 has five digits 56238 has five prime factors is there something in Oeis? I mean square free numbers N such that the number of digits of N equals the number of prime factors of N? 
20200828, 16:02  #3 
Aug 2006
2^{2}×1,493 Posts 
There are 10 terms with 10 prime factors:
6469693230, 6915878970, 8254436190, 8720021310, 9146807670, 9592993410 The largest prime factor among the terms is 467: 98070 = 2 * 3 * 5 * 7 * 467. 
20200828, 16:42  #4 
Mar 2018
17·31 Posts 
... 75894...
Pg(56238) is prime and also pg(75894) is prime
56238 and 75894 are multiple of 546. 56238 and 75894 are square free and belong to the Oeis sequence you mentioned Pg(n) is the concatenation in base ten of 2^n1 and 2^(n1)1 SO BECAuse the sequence oeis is finite, then pg(n) primes with n multiple of 546 should be not infinite Last fiddled with by enzocreti on 20200828 at 16:50 
20200828, 18:02  #5  
Mar 2018
17·31 Posts 
Quote:
Last fiddled with by enzocreti on 20200828 at 18:23 

20200829, 03:22  #6 
Aug 2006
2^{2}·1,493 Posts 

20200829, 08:01  #7 
Mar 2018
17·31 Posts 
... 56238...
56238 is a not palindromic number such that the reverse 83265 (squarefree) also belongs to Oeis sequence A165256. Are there other examples of not palindromic numbers belonging to A165256 whose reverse also belongs to A165256? Are there other squarefree non palindromic numbers belonging to A165256 whose reverse is squarefree and belongs to A165256?
Last fiddled with by enzocreti on 20200829 at 08:04 
20200829, 13:18  #8  
Feb 2017
Nowhere
1000011011010_{2} Posts 
Quote:
Hey there, lazybones! Using the plaintext exhaustive list provided at the OEIS page, I figured even a dunce at programming like me can tell PariGP to extract the answers. I tried it for practice. PariGP, in turn, yawned and rolled its eyes at being given such a trivial task, but delivered the results. If my code was writ right, the list of the smaller of each such pair in the sequence, whether either number in the pair is square free or not, is Code:
[12, 15, 26, 28, 36, 39, 45, 56, 57, 58, 68, 69, 132, 156, 165, 168, 204, 228, 246, 255, 258, 273, 276, 285, 286, 294, 366, 396, 408, 418, 426, 435, 438, 456, 465, 495, 498, 516, 528, 558, 588, 609, 618, 627, 638, 678, 759, 819, 1518, 2046, 2145, 2226, 2244, 2262, 2418, 2436, 2478, 2508, 2562, 2618, 2706, 2805, 2814, 2838, 2886, 2964, 3135, 3876, 3927, 4026, 4158, 4386, 4389, 4488, 4686, 4746, 4785, 4788, 4818, 4836, 4935, 4956, 5016, 5148, 5406, 5478, 5565, 5628, 5676, 5838, 5916, 5928, 6018, 6138, 6258, 6438, 6468, 6486, 6699, 6798, 7458, 8148, 8568, 15015, 23205, 24024, 24486, 24882, 26598, 26796, 27258, 42315, 45045, 45318, 48048, 54978, 55146, 56238, 57057, 58058, 58926, 59466, 60918, 62238, 64428, 66198, 68068, 68838, 69069, 78078, 80178, 82698, 88179, 204204, 228228, 246246, 255255, 258258, 285285, 408408, 435435, 438438, 456456, 465465, 491946, 498498, 516516, 558558, 585858, 618618, 678678, 686868] Code:
[15, 26, 39, 58, 165, 246, 285, 286, 366, 418, 435, 438, 498, 609, 759, 1518, 2046, 2226, 2262, 2418, 2478, 2618, 2814, 2838, 2886, 3135, 3927, 4386, 4389, 4746, 4785, 4935, 5406, 5478, 5565, 5838, 6018, 6438, 6486, 6699, 7458, 15015, 24486, 24882, 26598, 45318, 55146, 56238, 58058, 58926, 59466, 60918, 62238, 66198, 68838, 246246, 285285, 435435, 438438, 491946, 498498, 585858] Last fiddled with by Dr Sardonicus on 20200829 at 13:20 Reason: xifgin ostpy 

20200829, 18:31  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×3^{2}×7×37 Posts 
You guys are so easy to "snipe" (see this https://xkcd.com/356/ ).
When you deal with any enzocreti's posts, you have to remeber just 23 numbers (one of them "546"), and once you see any "science like" questions from him, always ask yourself "is this yet another inane attempt to predict the next member of his 'preciousss...' using small known members of the sequence, some of which happened to be multiples of 546?" If yes, simply check the tightness of the esteemed patient's garments and leave him alone. 
20200829, 19:02  #10  
Romulan Interpreter
Jun 2011
Thailand
9265_{10} Posts 
Quote:


20200829, 19:03  #11  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010001101100_{2} Posts 
Don't feel bad  I am easy to snipe too.
And I will dispense the single reason why periodicity easily enters the pg(n) sequence, and why it is apparent that it is a totally irrelevant distraction. Quote:
For an initial stretch of small k<104, one can write pg_1(k)=(2^k1)*10^((3*k+7)\10)+2^(k1)1 and for all PRPtestable testable numbers you can definitely write (...or something like that, I am typing on the fly. I will fix this later) pg_2(k)=(2^k1)*10^((3*k+7)\10+k\1000+k\33338)+2^(k1)1 pg_2(k) = pg(k) for all k<10^8 ...and then it isn't. But you cannot test there for primality anyway, so one can spend their life mucking with "properties" of pg_2(k) (which are obvious after spending 1015 minutes, modulos will be surely periodic and that will sieve out any possible candidates and the primes and PRPs will sit on invisible strings)  but it has nothing to do with "patterns" in real pg(k), which there will be none when k tends to infinity. ...And all talk (for a year, or is it more?) about "x less than a palindrome", "divisible by 546"... all vapors of a brain with high temperature. "Vanity of vanities, it is all vanity." (Eccl. 1:2) 

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