[seqfan] Naming advice

[Allan Wechsler]

I'm about to submit a sequence which I think is reasonably interesting, and
the only thing that is holding me up is lack of a good name. I'm hoping you
SeqFans can suggest something catchy.

For background, A034385 are the "primorials", the product of all primes not
exceeding N.

A108951, which I will call F(N) here, is a kind of extension to the
primorials. It agrees with A034385 when N is prime, and then uses the rule
that F(AB) = F(A)F(B) when the argument is composite. For example, F(18) =
F(2)F(3)F(3) = 2*6*6 = 72.

Now, it's a theorem (proof left to the reader for brevity) that all
ordinary factorials N! appear as F(K) for some K. My new sequence is
"Unique K such that F(K) = N!". If nobody comes up with a helpful name, my
fallback will have to be "Index of N! in A108951", but in general we don't
like to see sequence numbers in the names of other sequences.

What would really help is a good name for A108951(N). If F(N) were called
the "blerp" of N (not suggesting that seriously!) then my new sequence
would be the antiblerp of N factorial.

Notice that the entries in A108951 are all the least exemplars of their
prime signatures, so it is a permutation of A025487. These important
numbers are listed in "number-theoretic" order in the former sequence, and
in order of size in the latter.

I welcome any ideas. There are actually a bunch of sequences waiting to be
entered, based on the fact that a lot of sequences are subsets of A025487,
and tend to be awkwardly large (like factorials) -- their "antiblerps" are
usually much smaller and provide a sort of outline of the factorization of
the original number.