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%I #6 Mar 08 2023 23:17:19
%S 0,0,0,1,0,1,0,1,1,1,0,1,0,1,1,2,0,1,0,1,1,1,0,2,1,1,1,1,0,1,0,2,1,1,
%T 1,2,0,1,1,2,0,1,0,1,1,1,0,2,1,1,1,1,0,2,1,2,1,1,0,2,0,1,1,3,1,1,0,1,
%U 1,1,0,2,0,1,1,1,1,1,0,2,2,1,0,2,1,1,1
%N Half the number of prime factors of n (counted with multiplicity, A001222), rounded down.
%e The prime indices of 378 are {1,2,2,2,4}, so a(378) = floor(5/2) = 2.
%t Table[Floor[PrimeOmega[n]/2],{n,100}]
%Y Positions of 0's are 1 and A000040.
%Y Positions of first appearances are A000302 = 2^(2k) for k >= 0.
%Y Positions of 1's are A168645.
%Y Rounding up instead of down gives A360617.
%Y A112798 lists prime indices, length A001222, sum A056239, median* A360005.
%Y A360673 counts multisets by right sum (exclusive), inclusive A360671.
%Y First for prime indices, second for partitions, third for prime factors:
%Y - A360676 gives left sum (exclusive), counted by A360672, product A361200.
%Y - A360677 gives right sum (exclusive), counted by A360675, product A361201.
%Y - A360678 gives left sum (inclusive), counted by A360675, product A347043.
%Y - A360679 gives right sum (inclusive), counted by A360672, product A347044.
%Y Cf. A001248, A026424, A280076, A359912, A360006, A360457, A360674.
%K nonn
%O 1,16
%A _Gus Wiseman_, Mar 08 2023
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