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Forum: Aliquot Sequences 2021-03-04, 15:45
Replies: 949
Views: 69,196
Posted By warachwe
38^(12*19) has next term...

38^(12*19) has next term (http://factordb.com/sequences.php?se=1&aq=38%5E%2812*19%29&action=range&fr=0&to=20) as 3*5*7*13*229*457*C353. As the composite has no small factor, this is not abundant.
Forum: FactorDB 2020-11-20, 01:47
Replies: 54
Views: 8,411
Posted By warachwe
This is what I guess was happened. On 15th...

This is what I guess was happened.
On 15th November, someone enter a number of form bn with b<20000 and n<1000 or somewhere around that ballpark. Since then DB slowly determined whether each number...
Forum: FactorDB 2020-11-15, 21:16
Replies: 54
Views: 8,411
Posted By warachwe
I notice that most of the new number is of the...

I notice that most of the new number is of the form a^n+-1 for 10001<=a<=20000 and n somewhere around 20. Most of these numbers already factored at cownoise.com . Is there anyway to just transfered...
Forum: Aliquot Sequences 2020-09-14, 09:44
Replies: 949
Views: 69,196
Posted By warachwe
The problem seem to affect only n that is divided...

The problem seem to affect only n that is divided by some prime bigger than 50. Somehow it change 72^n to 2^(6*n).
Forum: Aliquot Sequences 2020-08-22, 11:03
Replies: 949
Views: 69,196
Posted By warachwe
Personally, I think these conjectures are...

Personally, I think these conjectures are interesting in a way that the prove seem somewhat doable, but I agree that we should look more into other phenomena.



I think I found a way.
S(24k) =...
Forum: Aliquot Sequences 2020-08-20, 18:56
Replies: 949
Views: 69,196
Posted By warachwe
From post #364 for p prime, s(pi) =...

From post #364


for p prime, s(pi) = (pi-1)/(p-1) and s(p(i*n)) = (p(i*n)-1)/(p-1).

Since (pi-1) is a factor of (p(i*n)-1), s(pi) is a factor of s(p(i*n)) for all positive integer n.

for...
Forum: Aliquot Sequences 2020-08-20, 18:30
Replies: 949
Views: 69,196
Posted By warachwe
Sure :smile: Those conjectures may...

Sure :smile:



Those conjectures may still be true, because we can still get a factor of 79 from other primes than 157.
For example, from conjecture 2), normally 5 is what provide a factor of 3...
Forum: Aliquot Sequences 2020-08-20, 03:45
Replies: 949
Views: 69,196
Posted By warachwe
I forgot to mention that q^2 also must not divide...

I forgot to mention that q^2 also must not divide n, or else p may not divide s(n).



So in this case, for s(s(s(n))) may not be divided by 79 if, for example, s(s(n)) got a factor of 157^2, but...
Forum: Aliquot Sequences 2020-08-19, 16:25
Replies: 949
Views: 69,196
Posted By warachwe
For p prime, s(p^k) is (p^k-1)/(p-1). So...

For p prime, s(p^k) is (p^k-1)/(p-1). So S(3^(6+12*k)) is (3^(6+12*k)-1)/2, which is (3^6-1)/2 * (3^(12*k)+3^(12k-6)+3^(12k-12)...+1)

So s(n) divided by (3^6-1)/2 = 364 = 2^2 *7 * 13.

As 3^6 is...
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