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Ceiling of the mean of the prime factors of n (with multiplicity).
1

%I #13 Jul 23 2023 03:34:53

%S 0,2,3,2,5,3,7,2,3,4,11,3,13,5,4,2,17,3,19,3,5,7,23,3,5,8,3,4,29,4,31,

%T 2,7,10,6,3,37,11,8,3,41,4,43,5,4,13,47,3,7,4,10,6,53,3,8,4,11,16,59,

%U 3,61,17,5,2,9,6,67,7,13,5,71,3,73,20,5,8,9,6

%N Ceiling of the mean of the prime factors of n (with multiplicity).

%F Ceiling of A123528(n)/A123529(n).

%e The prime factors of 450 are {2,3,3,5,5}, with mean 18/5, so a(450) = 4.

%t prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];

%t Table[If[n==1,0,Ceiling[Mean[prifacs[n]]]],{n,100}]

%Y For median of prime indices we have triangle A124944, low A124943.

%Y The round version is A067629.

%Y The floor version is A126594.

%Y A027746 lists prime factors, indices A112798.

%Y A078175 lists numbers with integer mean of prime factors.

%Y A123528/A123529 gives mean of prime factors, A326567/A326568 prime indices.

%Y Cf. A026905, A051293, A316413, A327473, A327476, A327482, A363895, A363943, A363948, A363950, A364037.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 18 2023