# [seqfan] Re: A001055 Number of ways of factoring n with all factors>1

David Wilson dwilson at gambitcomm.com
Tue Mar 3 16:09:26 CET 2009

Subject to the erratum:

By factorization of n, we mean a multiset of integers >= 1 whose product is
n.

should be

By factorization of n, we mean a multiset of integers > 1 whose product is
n.

Joerg Arndt wrote:
> Shame on me for my earlier post...
>
> I agree with the argument below,
> please enter a comment into the sequence.
>
>
> * David Wilson <davidwwilson at comcast.net> [Mar 03. 2009 10:57]:
>
>> By factorization of n, we mean a multiset of integers >= 1 whose product is
>> n.
>>
>> For example, 6 is the product of 2 such multisets, {2, 3} and {6}, so
>> A001055(6) = 2.
>>
>> Similarly, 8 is the product of 3 such multisets, {2, 2, 2}, {2, 4} and {8},
>> so A001055(6) = 3.
>>
>> 1 is the product of 1 such multiset, namely the empty multiset {}, whose
>> product is by definition the multiplicative identity 1. Hence A001055(1) =
>> 1.
>>
>> In other words, a(1) = 1 is consistent with the definition.
>>
>>
>> [...]
>>
>
>
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