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

[rgwv at rgwv.com]

This is but a slight rearrangement of A078840.

-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Brad Klee
Sent: Friday, January 18, 2019 12:25 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Increasing, factor-count permutation of N/{0}.

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

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