[seqfan] Re: Q on multiplicative functions
maxale at gmail.com
Wed Feb 9 15:40:53 CET 2011
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)
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
> 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.
>> Seqfan Mailing list - http://list.seqfan.eu/
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