[seqfan] Re: Highly cototient numbers

[T. D. Noe]

At 9:57 AM -0400 3/15/10, Alonso Del Arte wrote:
>Yes, there should be at least one better technique. In 2004, just for the
>sake of having a program for
>A005277<http://www.research.att.com/~njas/sequences/A005277>,
>I sent in a Mathematica program that calculates phi(n) for each n up to 320.
>Then in 2006 it finally occurred to me that it would just be easier to
>calculate (p - 1)(q - 1) and such and then cull the numbers not in those
>sets. Of course the 2004 program can be made to go into larger numbers by
>simply changing searchMax, while with the 2006 program one would also have
>to take into account totients with more than three prime factors or else be
>ready to identify false positives.

Today I calculated 176 terms for this sequence, up to about 1.6 x 10^6.  I
will submit the b-file today, along with one for A101373, which counts the
number of solutions.

It appears that this sequence eventually has the same terms as the
Goldbach-related sequence A082917 (numbers n with property that n can be
written in more ways as a sum of two odd primes than any smaller even
number).  In fact, the last 69 highly cototient numbers match 69
consecutive terms of A082917, which will have a b-file of terms up to 10^7
soon.

Tony