[seqfan] Re: Prime signature of 1, and second signature

David Wilson davidwwilson at comcast.net
Mon Jun 11 00:00:35 CEST 2012

I did not invent the phrase "prime signature," nor do I remember where I 
heard it. At the time I submitted A025487, I understood it to be the 
correct terminology.

I certainly did not define the concept. The term "prime signature of n" 
is shorthand for "the exponents in the prime factorization of n counted 
with multiplicity," an idea that has been around for centuries. At least 
as far back as the 1700's it has been known how to compute the number of 
divisors of n from the exponents in the prime factorization of n 
(without knowing the primes). Today we might say "tau(n) is a function 
of the prime signature of n" but this is mere semantics, not a 
conceptual leap.

On 6/10/2012 3:06 PM, Matthew Vandermast wrote:
> Thanks, David.  I've been curious about the history of the phrase "prime signature." Did you invent the phrase and/or first define the concept? If so, my hat is off to you (if not, my hat is still off just for submitting the sequence, which is perhaps my favorite in the database).  I was also influenced by your A001055 comment when writing my original e-mail about this.

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