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a(n) = 2*omega(n) - bigomega(n).
8

%I #16 Oct 01 2023 02:32:49

%S 0,1,1,0,1,2,1,-1,0,2,1,1,1,2,2,-2,1,1,1,1,2,2,1,0,0,2,-1,1,1,3,1,-3,

%T 2,2,2,0,1,2,2,0,1,3,1,1,1,2,1,-1,0,1,2,1,1,0,2,0,2,2,1,2,1,2,1,-4,2,

%U 3,1,1,2,3,1,-1,1,2,1,1,2,3,1,-1,-2,2,1,2

%N a(n) = 2*omega(n) - bigomega(n).

%H Amiram Eldar, <a href="/A361205/b361205.txt">Table of n, a(n) for n = 1..10000</a>

%F Additive with a(p^e) = 2 - e. - _Amiram Eldar_, Mar 26 2023

%F Sum_{k=1..n} a(k) = n * log(log(n)) + c * n + O(n/log(n)), where c = 2*A077761 - A083342 = A077761 - A136141 = -0.511659... . - _Amiram Eldar_, Oct 01 2023

%t Table[2*PrimeNu[n]-PrimeOmega[n],{n,100}]

%Y Without doubling omega we have -A046660.

%Y Positions of 0's are A067801, counted by A239959.

%Y Positions of negative terms are A360558, counted by A360254.

%Y Positions of nonpositive terms are A361204, counted by A237363.

%Y Positions of positive terms are A361393, counted by A237365.

%Y Positions of nonnegative terms are A361395, counted by A361394.

%Y A001221 (omega) counts distinct prime factors.

%Y A001222 (bigomega) counts prime factors.

%Y A112798 lists prime indices, sum A056239.

%Y Cf. A061395, A067340, A111907, A324517, A324522, A326567/A326568.

%Y Cf. A077761, A083342, A136141.

%K sign,easy

%O 1,6

%A _Gus Wiseman_, Mar 16 2023