A360617 Half the number of prime factors of n (counted with multiplicity, A001222), rounded up.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Mar 08 2023

Keywords

• nonn

Examples

			The prime indices of 378 are {1,2,2,2,4}, so a(378) = ceiling(5/2) = 3.
		

Crossrefs

Positions of 0's and 1's are 1 and A037143.

Positions of first appearances are A081294.

Rounding down instead of up gives A360616.

A112798 lists prime indices, length A001222, sum A056239, median* A360005.

A360673 counts multisets by right sum (exclusive), inclusive A360671.

First for prime indices, second for partitions, third for prime factors:

- A360676 gives left sum (exclusive), counted by A360672, product A361200.

- A360677 gives right sum (exclusive), counted by A360675, product A361201.

- A360678 gives left sum (inclusive), counted by A360675, product A347043.

- A360679 gives right sum (inclusive), counted by A360672, product A347044.

Cf. A000040, A000302, A001248, A026424, A168645, A359912, A360006, A360457.

Programs

Mathematica

Table[Ceiling[PrimeOmega[n]/2],{n,100}]