[seqfan] Re: A007987 ? was Re: Re: Number of solutions of a*b + c*d + ... + y*z = 0 (mod n)

[Max Alekseyev]

The formula for this new sequence is

a(n) = ( A000010(n) + A060594(n) ) / 2

Regards,
Max

On Mon, Sep 6, 2010 at 9:17 PM, Ron Hardin <rhhardin at att.net> wrote:
> This (new) matches A007897 a lot, but not quite always
>
>  0,1,2,2,3,2,4,4,4,3,6,4,7,4,6,6,9,4,10,6,8,6,12,8,11,7,10,8,15,6,16,10,
>  12,9,14,8,19,10,14,12,21,8,22,12,14,12,24,12,22,11,18,14,27,10,22,16,20,
>  15,30,12,31,16,20,18,26,12,34,18,24,14,36,16,37,19,22,20,32,14,40,20,28
>  Number of distinct no-zero solutions of sum{i=1..1}(x(2i-1)*x(2i)) = 1 (mod n)
>  Column 1 of AYYYYYY
>  Solutions for product of a single 1..10 pair = 1 (mod 11) are
>  (5*9) (2*6) (3*4) (1*1) (7*8) (10*10)
>  <a href="b000011.txt">Table of n, a(n) for n=1..8248</a>
>
> vs.
>
> A007897 phi(n), where phi(n) is multiplicative with phi(2) = 1; phi(4) = 2;
> phi(2^a) = 2^(a-2)+2 if a>2; phi(p^a) = (p-1)*p^(a-1)/2 if prime  p>2 and a>0.
>
> 1, 1, 2, 2, 3, 2, 4, 4, 4, 3, 6, 4, 7, 4, 6, 6, 9, 4, 10, 6, 8, 6,  12, 8, 11,
> 7, 10, 8, 15, 6, 16, 10, 12, 9, 12, 8, 19, 10, 14, 12, 21, 8,  22, 12, 12, 12,
> 24, 12, 22, 11, 18, 14, 27, 10, 18, 16, 20, 15, 30, 12,  31, 16, 16, 18, 21, 12,
> 34, 18, 24, 12, 36, 16, 37, 19, 22, 20, 24, 14,  40, 18, 28
>
> is there any reason to expect them to be the same?
>
>
>
>
>  rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>
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