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A362983 Number of prime factors of n (with multiplicity) that are greater than the least.

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%I A362983 #6 May 18 2023 23:26:26
%S A362983 0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,2,0,1,1,1,0,1,0,1,0,1,0,2,0,0,1,1,
%T A362983 1,2,0,1,1,1,0,2,0,1,1,1,0,1,0,2,1,1,0,3,1,1,1,1,0,2,0,1,1,0,1,2,0,1,
%U A362983 1,2,0,2,0,1,2,1,1,2,0,1,0,1,0,2,1,1,1
%N A362983 Number of prime factors of n (with multiplicity) that are greater than the least.
%F A362983 a(n) = A001222(n) - A067029(n).
%F A362983 a(n) = A001222(A028234(n)).
%e A362983 The prime factorization of 360 is 2*2*2*3*3*5, with factors greater than the least 3*3*5, so a(360) = 3.
%t A362983 Table[PrimeOmega[n]-If[n==1,0,FactorInteger[n][[1,2]]],{n,30}]
%Y A362983 Positions of 0's are A000961.
%Y A362983 Positions of numbers > 0 are A024619.
%Y A362983 Positions of first appearances appear to be A099856.
%Y A362983 For "less than greatest" instead of "greater than least" we have A325226.
%Y A362983 For multiplicities instead of parts we have A363131.
%Y A362983 A027746 lists prime factors, A112798 indices, A124010 exponents.
%Y A362983 A047966 counts uniform partitions, ranks A072774.
%Y A362983 A363128 counts partitions with more than one non-mode, complement A363129.
%Y A362983 Cf. A001221, A001222, A052126, A053585, A061395, A064989, A071178, A105441, A307517, A325230.
%K A362983 nonn
%O A362983 1,18
%A A362983 _Gus Wiseman_, May 18 2023