[seqfan] Moebius-transform of A005187 ?

[Antti Karttunen]

Consider the sequences A035532 and A297111:

https://oeis.org/search?q=+%091%2C+2%2C+3%2C+4%2C+7%2C+4%2C+10%2C+8%2C+12%2C+8%2C+18%2C+8%2C+22%2C+12&sort=&language=&go=Search

The latter is Moebius-transform of A005187 I recently submitted, while from
the formula-section of the former: G.f.: Sum A005187(n) x^n = Sum
a(n)*x^n/(1-x^n)
it seems to me that it also claims to be Möbius-transform of A005187. (See
e.g.
https://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula#Series_relations
)
However, the sequences differ for the first time at n=15, although even
after that they seem to contain many identical terms.

(Moreover, is there an indexing mismatch in Zumkeller's formula a(n) =
2*A000010(n) - A010051(n)*A048881(n) ?)


Now, I just wonder where this "slightly flawed" insight in A035532 stems
from, and on what specific n it fails: 15, 21, 25, 27, 33, 35, 51,  ...
(where two sequences differ, "manually tallied" so beware) and why?



Best regards,

Antti