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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.
8
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
1,2
COMMENTS
First differs from A304678 in having 300.
EXAMPLE
The prime factorization of 300 is 2*2*3*5*5, with modes {2,5} and maximum 5, so 300 is in the sequence.
MATHEMATICA
prifacs[n_]:=If[n==1, {}, Flatten[ConstantArray@@@FactorInteger[n]]];
Select[Range[100], MemberQ[Commonest[prifacs[#]], Max[prifacs[#]]&]
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.
Sequence in context: A316529 A329138 A334969 * A065200 A342526 A325361
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 09 2023
STATUS
approved