A362619 One and all numbers whose greatest prime factor is a mode, meaning it appears at least as many times as each of the others.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83

Offset: 1

Author

Gus Wiseman, May 09 2023

Keywords

• nonn

Comments

First differs from A304678 in having 300.

Examples

			The prime factorization of 300 is 2*2*3*5*5, with modes {2,5} and maximum 5, so 300 is in the sequence.
		

Links

• Wikipedia, Mode (statistics).

Crossrefs

Partitions of this type are counted by A171979.

The case of a unique mode is A362616, counted by A362612.

The complement is A362620, counted by A240302.

A027746 lists prime factors, A112798 indices, length A001222, sum A056239.

A356862 ranks partitions with a unique mode, counted by A362608.

A359178 ranks partitions with a unique co-mode, counted by A362610.

A362605 ranks partitions with a more than one mode, counted by A362607.

A362606 ranks partitions with a more than one co-mode, counted by A362609.

A362611 counts modes in prime factorization, triangle version A362614.

A362613 counts co-modes in prime factorization, triangle version A362615.

A362621 ranks partitions with median equal to maximum, counted by A053263.

Cf. A000040, A002865, A237824, A237984, A327473, A327476, A359908.

Programs

Mathematica

prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
Select[Range[100],MemberQ[Commonest[prifacs[#]],Max[prifacs[#]]]&]