Q3. Find \(\displaystyle \sum_{n=1}^{2520}\gcd(n,2520).\)
Bonus: Do it without using a computer.
Bonus: Do it without using a computer.
Well, if they weren't all integers, then it wouldn't be a sequence in the OEIS then!CRGreathouse said:Why are all terms of A234566 integers?
Well, two key components are that the Fibonacci sequence is a gcd sequence: gcd(F(m), F(n)) = F(gcd(m, n)) and that Fibonacci numbers greater than, uh, 144 have a primitive prime divisor: p | F(n) but p does not divide F(m) for 0 < m < n. So sometimes you find that two factors are 'stuck together' for Fibonacci sequences and you can't get them apart, which means you can't make those numbers separately.johnr said:Messing with the Fibonacci question empirically cost me hours of sleep! The more I sought, the more I found. Anyone get anywhere interesting with it?
Yes, please!agentredlum said:Please allow me to post a question.
Well, my first guess would be that this is an indicator sequence representing the primes 2, 3, 5, 13, 17, 113, ....agentredlum said:Q. Find a relation between primes that generates the first 31 numbers in the following integer sequence
1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ...
Thank you for participating! From the primes you give above , only 17 and one more prime are represented in the sequence. I don't want to say too much yet for fear of making it too easy , but of course i will be happy to say more if you or anyone else asks.CRGreathouse said:Well, my first guess would be that this is an indicator sequence representing the primes 2, 3, 5, 13, 17, 113, ....agentredlum said:Q. Find a relation between primes that generates the first 31 numbers in the following integer sequence
1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 ...
I don't think it is related to prime gaps in the usual sense , for example , the prime gap between 23 and 29 is 6 because 29 - 23 = 6 (I personally disagree with the definition but that's niether here nor there :mrgreenCRGreathouse said:If so, I might further guess that this is related to prime gaps, since 113 is the first prime before a record gap (the next prime is 113 + 14 = 127). But I can't get any further, even if both are right.