A364156 Ceiling of the mean of the prime factors of n (with multiplicity).

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

Offset: 1

Author

Gus Wiseman, Jul 18 2023

Keywords

• nonn

Examples

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

Crossrefs

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

The round version is A067629.

The floor version is A126594.

A027746 lists prime factors, indices A112798.

A078175 lists numbers with integer mean of prime factors.

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

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

Programs

Mathematica

prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
Table[If[n==1,0,Ceiling[Mean[prifacs[n]]]],{n,100}]

Formula

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