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

1,2

Links

Table of n, a(n) for n=1..78.

Formula

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

Example

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

Mathematica

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

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.

Sequence in context: A218993 A067629 A079870 * A185642 A076690 A262549

Adjacent sequences: A364153 A364154 A364155 * A364157 A364158 A364159

Keyword

nonn

Author

Gus Wiseman, Jul 18 2023

Status

approved