[seqfan] Re: Naming advice

[Marc LeBrun]

>=Allan Wechsler <acwacw at gmail.com>:
> What would really help is a good name for A108951(N)

Alan, interesting ideas.  I can't think of a good name that's both conventional and succinct.  Maybe try this?

A108951(N) could be described as "Replace p in the prime factorization [or decomposition?] of N with p#".
Based on this it would seem its name should be an instance of class of analogs that work for different values of "p#".

Assuming you're OK with coining some terse new terminology, we could call these "[prime] RECOMPOSITIONS".
(since the transform is built around the reverse of the prime decomposition)

Hence A108951(N) would be the "primorial [prime] recomposition of N".
(and presumably similarly for any other values of "p#" that arise)

So a brief name for your new sequence might be "n such that the primorial [prime] recomposition of n is a factorial"...


Alternatively, "totally multiplicative" sequences might be called the "[multiplicative] COMPLETION" [or cover?] of their values at primes 
(that is, TM is a property that *completely* (like, totally, man) specifies the construction of all the composite values)
Then your new sequence could be named "n such that the primorial [multiplicative] completion of n is a factorial"...

Hope this helps...