# [seqfan] Re: multiplicative set-like sequences

David Wilson davidwwilson at comcast.net
Sat Feb 26 18:19:16 CET 2011

```I don't think it wise to add a keyword for every conceivable property a
sequence might have.

How about "property pages" (P-pages, numbered just like sequences)? The
property page for multiplicative sequences might (initially) look like:

------------------------------------------
Multiplicative Sequences

A multiplicative sequence is a sequence defined on the positive integers
which obeys the relation

a(mn) = a(m)a(n),  if gcd(m, n) = 1.

Properties:

a(1) = 1.

a(PROD(p_i^e_i)) = PROD(a(p_i^e_i)).

A multiplicative sequence is determined by its values p^e where p is
prime and e >= 1. If n has the prime factorization
n = PROD(p^e), then a(n) = PROD(a(p^e)).

Sequence description:

%C A123456 <a href="property/multiplicative.htm">Multiplicative</a>

If you also know its values at prime powers, create a formula line:

%F A123456 <a href="property/multiplicative.htm">Multiplicative</a>
with a(p^e) = e+1.

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