A362620 - OEIS

A362620

Numbers whose greatest prime factor is not a mode, meaning it appears fewer times than some other.

12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 63, 68, 72, 76, 80, 84, 88, 90, 92, 96, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 200, 204, 207, 208, 212

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

First differs from A112769 in lacking 300.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Wikipedia, Mode (statistics).

EXAMPLE

The prime factorization of 90 is 2*3*3*5, with modes {3} and maximum 5, so 90 is in the sequence.

MAPLE

filter:= proc(n) local F;

F:= sort(ifactors(n)[2], (a, b) -> a[1]<b[1]);

F[-1, 2] < max(F[.., 2])

end proc:

select(filter, [$2..300]); # Robert Israel, Dec 15 2023

MATHEMATICA

prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];

Select[Range[2, 100], FreeQ[Commonest[prifacs[#]], Max[prifacs[#]]]&]

CROSSREFS

Partitions of this type are counted by A240302.

The complement is A362619, counted by A171979.

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, A362616.

Sequence in context: A361868 A316597 A329142 * A112769 A360253 A097320

Adjacent sequences: A362617 A362618 A362619 * A362621 A362622 A362623

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 11 2023

STATUS

approved