[seqfan] Re: Q on multiplicative functions

[Max Alekseyev]

A160467 is multiplicative.
That's easily follows from the formula
A160467(n) = 2^max(valuation(n,2)-1,0)

Now if co-prime m,n are both odd, then
A160467(m) = A160467(n) = A160467(m*n) = 1,
trivially implying that A160467(m*n) = A160467(m) * A160467(n).

If one of co-prime m,n is even (say, m), then A160467(n) = 1 and thus
A160467(m*n) = A160467(m) = A160467(m)*A160467(n)

Regards,
Max

On Mon, Feb 7, 2011 at 5:56 PM, Charles Greathouse
<charles.greathouse at case.edu> wrote:
> To avoid duplication of effort:
>
> A151764 is completely multiplicative.  I edited the sequence
>
> A163659 and A160467 appear to be multiplicative but I haven't proved
> it.  The first 10,000 terms are multiplicative.
>
> I don't understand A157261 or A159631.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Mon, Feb 7, 2011 at 8:58 AM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
>>
>> Are these multiplicative functions?
>>
>> <a href="http://oeis.org/A151764">A151764</a>
>>  This is a repeated application of a multiplicative function
>>
>> <a href="http://oeis.org/A157261">A157261</a>
>>  lengths of blocks of 2 in Gijswijt's sequence
>>
>> <a href="http://oeis.org/A159631">A159631</a>
>> <a href="http://oeis.org/A159634">A159634</a> 1 ?
>>  dimension of a space of modular forms
>>
>> <a href="http://oeis.org/A160467">A160467</a>
>>  2 to some power involving sigma() and oddness
>>  (this might be a product of two multiplicative functions...)
>>
>> <a href="http://oeis.org/A163659">A163659</a>
>>  Defined as a logarithmic g.f. of Stern's diatomic series
>>
>> I am asking because they do not have the keyword:mult yet.
>>
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>>
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