[seqfan] A mysterious sequence found accidentally by analysis of a recycled draft.

[Thomas Scheuerle]

Dear sequence fans, 

Recently a draft from Dylan A. Elias got recycled because it was abandoned.
It did not contain complete information to reproduce it numbers.
I was curious and looked into it and its description suggested to me something 
which I did put into a PARI program here:

a(n) = if(n=0, 1, log(abs(I*(1-I)*prod(k = 1, n, 1-I^prime(k))^prime(n))^2)/log(2))

It gives the sequence:
1,5,10,21,36,67,92,137,172,231,320,373,482,575,646,753,902,1063,1160,1341,1492,1607,1818,1993,2226,2523,2728,2885,3104,3271,3504,4065,...

This is not the same sequence the author did originally propose as I failed to reproduce or understand the idea properly.

This sequence is for me mysterious and puzzling, could it be interesting?
It has odd and even terms interleaved.
A084310(n) = gcd(n,a(n)) appears to hold by observation.
Does anyone know into which topic this sequence may belong?

thank you very much

Thomas