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

David Wilson davidwwilson at comcast.net
Sun Mar 1 07:01:34 CET 2009

```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.

----- Original Message -----
From: "N. J. A. Sloane" <njas at research.att.com>
To: <seqfan at list.seqfan.eu>; <seqfan at seqfan.eu>
Cc: <njas at research.att.com>
Sent: Saturday, February 28, 2009 3:02 PM
Subject: [seqfan] Re: A001055 Number of ways of factoring n with all
factors>1

> Dear Maximilian,   the INTENT of this sequence,
> and the way it is described in the 1973 and 1995 books,
> is Number of ways of factoring n.
>
> The phrase "with all factors >1" was added later.
>
> That phrase needs to be modified, and I will do so.
>
> But a(1) = 1 is what I wanted, and that doesn't need changing!
>
>
> Best regards
>  Neil
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

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