[seqfan] Increasing, factor-count permutation of N/{0}.

[Brad Klee]

Hi Seqfans,

A069281, thanks to Jason Kimberly, cross references three
historically separate runs through "almost primes", of course
tending to become less and less prime as time goes on with
each successive author and each successive contribution.

I didn't check for the 21-almost primes. At some integer n it
becomes absurd to search out every sequence of n-almost
primes.

Wouldn't it be better to have just one triangular sequence?

T(n,k), read by antidiagonals, gives the n^th smallest counting
number with length-k prime factorization; n>0,k>0.

1,   4,    8,     16,    32,
2,   6,    12,    24,   48,
3,   9,    18,    36,   72,
5,   10,   20,   40,    80
7,   14,   27,   54,   108
...

The search for "1,2,4,3,6,8,5,9,12,16" returns a null result--
no mention of any one of the 20 almost-prime sequences.

Typically I am not that interested in factoring, primes,
almost-primes, whatever, but if anyone thinks this
permutation is worth adding, I will type out the entry.

Do we also have a decision on the general question?
Given a sequence-valued function of N, should we create,
say, 20 separate entries, or simply have a convention for
listing the values in a table / triangle? ( Cf. A060539 )

Cheers,

Brad