Number-Divisors Almost = ln(m) + 2c-1

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Leroy Quet <qq-quet at mindspring.com> schrieb am 02.12.2003, 03:18:11:

<<
what is the sequence of increasing positive integers where: 

a(1) = 1; 

|d(a(m)) - ln(a(m)) +1 -2c|  < 

|d(a(m-1)) - ln(a(m-1)) +1 -2c| 


for all m >= 2 ? 
>>

I checked from 2..128 and found records for
 3: 2 -  ln(3) +1 -2*0.5772156649=0.746956382
 5: 2 -  ln(5) +1 -2*0.5772156649=0.236130758
 7: 2 -  ln(7) +1 -2*0.5772156649=-0.100341479
46: 4 - ln(46) +1 -2*0.5772156649=0.016927274

Should be very easy to extend this with Maple's tau,
Mathematica's DivisorSigma or Pari's numdiv ...?

Hugo Pfoertner