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Number of prime factors of n that are less than the largest, counted with multiplicity.
5

%I #10 Nov 17 2019 22:39:17

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

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

%U 1,2,0,3,0,1,1,2,1,2,0,4,0,1,0,3,1,1,1,3,0,3,1,2,1,1,1,5,0,1,2,2,0,2,0,3,2

%N Number of prime factors of n that are less than the largest, counted with multiplicity.

%H Antti Karttunen, <a href="/A325226/b325226.txt">Table of n, a(n) for n = 1..100000</a>

%F a(n) = A001222(n/A053585(n)).

%F a(n) = A001222(n) - A071178(n) = A062977(A108951(n)). - _Antti Karttunen_, Nov 17 2019

%e The prime factors of 300 are {2,2,3,5,5} of which {2,2,3} are less than the largest, so a(300) = 3.

%t Table[PrimeOmega[n/Power@@FactorInteger[n][[-1]]],{n,100}]

%o (PARI)

%o A071178(n) = if(1==n, 0, factor(n)[omega(n), 2]);

%o A325226(n) = (bigomega(n) - A071178(n)); \\ _Antti Karttunen_, Nov 17 2019

%Y Positions of 0's are A000961. Positions of 1's are A325230. Positions of terms > 1 are A307517.

%Y Cf. A000094, A000245, A001222, A052126, A053585, A061395, A062977, A064989, A071178, A105441, A108951, A256617.

%K nonn

%O 1,12

%A _Gus Wiseman_, Apr 12 2019

%E Data section extended up to term a(105) by _Antti Karttunen_, Nov 17 2019