cp's OEIS Frontend

A362618 Numbers whose prime factorization has either (1) odd length, or (2) equal middle parts.

%I A362618 #9 May 11 2023 08:47:00
%S A362618 2,3,4,5,7,8,9,11,12,13,16,17,18,19,20,23,24,25,27,28,29,30,31,32,37,
%T A362618 40,41,42,43,44,45,47,48,49,50,52,53,54,56,59,61,63,64,66,67,68,70,71,
%U A362618 72,73,75,76,78,79,80,81,83,88,89,90,92,96,97,98,99,101
%N A362618 Numbers whose prime factorization has either (1) odd length, or (2) equal middle parts.
%C A362618 Also numbers n whose median prime factor is a prime factor of n.
%e A362618 The prime factorization of 90 is 2*3*3*5, with middle parts (3,3), so 90 is in the sequence.
%t A362618 prifacs[n_]:=If[n==1,{},Flatten[ConstantArray@@@FactorInteger[n]]];
%t A362618 Select[Range[2,100],MemberQ[prifacs[#],Median[prifacs[#]]]&]
%Y A362618 Partitions of this type are counted by A238478.
%Y A362618 The complement (without 1) is A362617, counted by A238479.
%Y A362618 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A362618 A359178 ranks partitions with a unique co-mode, counted by A362610.
%Y A362618 A359893 counts partitions by median.
%Y A362618 A359908 ranks partitions with integer median, counted by A325347.
%Y A362618 A359912 ranks partitions with non-integer median, counted by A307683.
%Y A362618 A362611 ranks modes in prime factorization, counted by A362614.
%Y A362618 A362621 ranks partitions with median equal to maximum, counted by A053263.
%Y A362618 A362622 ranks partitions whose maximum is a middle part, counted by A237824.
%Y A362618 Cf. A000040, A171979, A327473, A327476, A356862, A359907, A360686, A360952, A362616, A362620.
%K A362618 nonn
%O A362618 1,1
%A A362618 _Gus Wiseman_, May 10 2023