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A362620
Numbers whose greatest prime factor is not a mode, meaning it appears fewer times than some other.
7
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
OFFSET
1,1
COMMENTS
First differs from A112769 in lacking 300.
LINKS
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.
Sequence in context: A361868 A316597 A329142 * A112769 A360253 A097320
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 11 2023
STATUS
approved