A362619 revision #3
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A362619
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Numbers whose greatest prime factor is a mode, meaning it appears at least as many times as each of the others.
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8
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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
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OFFSET
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1,2
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COMMENTS
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First differs from A304678 in having 300.
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LINKS
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EXAMPLE
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The prime indices of 300 are {1,1,2,3,3}, with modes {1,3} and maximum 3, so 300 is in the sequence.
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], #==1||MemberQ[Commonest[prix[#]], Max[prix[#]]]&]
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CROSSREFS
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Partitions of this type are counted by A171979.
The case where the maximum is the only mode is A362616, counted by A362612.
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.
A362621 ranks partitions with median equal to maximum, counted by A053263.
Cf. A000040 pri, A000720 pri_pi, A002865 ptns_multimax, A098859 ptns_dstnct_mults, A215366 h_tri, A237824 ptns_twi_min_geq_max, A237984 ptns_mean_is_part, A275870 collapsible, A327473 h_mean_is_part, A327476 h_ptns_wo_mean, A359908 prix_int_medn.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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editing
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