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a(n) = bigomega(n) - mu(n).
1

%I #12 Sep 08 2022 08:46:19

%S -1,2,2,2,2,1,2,3,2,1,2,3,2,1,1,4,2,3,2,3,1,1,2,4,2,1,3,3,2,4,2,5,1,1,

%T 1,4,2,1,1,4,2,4,2,3,3,1,2,5,2,3,1,3,2,4,1,4,1,1,2,4,2,1,3,6,1,4,2,3,

%U 1,4,2,5,2,1,3,3,1,4,2,5,4,1,2

%N a(n) = bigomega(n) - mu(n).

%H Vincenzo Librandi, <a href="/A289641/b289641.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001222(n) - A008683(n).

%t Table[PrimeOmega[k] - MoebiusMu[k], {k, 1, 100}]]

%o (Magma) [n eq 1 select -1 else &+[p[2]: p in Factorization(n)]- MoebiusMu(n): n in [1..120]];

%o (PARI) a(n)=my(f=factor(n)); bigomega(f)-moebius(f) \\ _Charles R Greathouse IV_, Jul 09 2017

%Y Cf. A001222, A008683, A249901.

%K sign

%O 1,2

%A _Vincenzo Librandi_, Jul 09 2017