A361200 Product of the left half (exclusive) of the multiset of prime factors of n; a(1) = 0.

0, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 1, 4, 5, 2, 3, 2, 1, 2, 1, 4, 3, 2, 5, 4, 1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 1, 4, 7, 2, 3, 2, 1, 6, 5, 4, 3, 2, 1, 4, 1, 2, 3, 8, 5, 2, 1, 2, 3, 2, 1, 4, 1, 2, 3, 2, 7, 2, 1, 4, 9, 2, 1, 4, 5, 2, 3

Offset

1,4

Links

Table of n, a(n) for n=1..87.

Formula

A361200(n) * A347044(n) = n.

A361201(n) * A347043(n) = n.

Example

The prime factors of 250 are {2,5,5,5}, with left half (exclusive) {2,5}, with product 10, so a(250) = 10.

Mathematica

Table[If[n==1, 0, Times@@Take[Join@@ConstantArray@@@FactorInteger[n], Floor[PrimeOmega[n]/2]]], {n, 100}]

Crossrefs

Positions of 1's are A000040.

Positions of 2's are A037143.

The inclusive version is A347043.

The right inclusive version A347044.

The right version is A361201.

A000005 counts divisors.

A001221 counts distinct prime factors.

A006530 gives greatest prime factor.

A112798 lists prime indices, length A001222, sum A056239.

A360616 gives half of bigomega (exclusive), inclusive A360617.

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. A001248, A026424, A096825, A347045, A347046, A360005.

Sequence in context: A322813 A366189 A137866 * A329888 A352202 A266161

Adjacent sequences: A361197 A361198 A361199 * A361201 A361202 A361203

Keyword

nonn

Author

Gus Wiseman, Mar 10 2023

Status

approved