A362983 - OEIS

%I #6 May 18 2023 23:26:26

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

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

%F a(n) = A001222(n) - A067029(n).

%F a(n) = A001222(A028234(n)).

%e 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 Table[PrimeOmega[n]-If[n==1,0,FactorInteger[n][[1,2]]],{n,30}]

%Y Positions of 0's are A000961.

%Y Positions of numbers > 0 are A024619.

%Y Positions of first appearances appear to be A099856.

%Y For "less than greatest" instead of "greater than least" we have A325226.

%Y For multiplicities instead of parts we have A363131.

%Y A027746 lists prime factors, A112798 indices, A124010 exponents.

%Y A047966 counts uniform partitions, ranks A072774.

%Y A363128 counts partitions with more than one non-mode, complement A363129.

%Y Cf. A001221, A001222, A052126, A053585, A061395, A064989, A071178, A105441, A307517, A325230.

%K nonn

%O 1,18

%A _Gus Wiseman_, May 18 2023