cp's OEIS Frontend

A361868 Positive integers > 1 whose prime indices satisfy (maximum) >= 2*(median).

%I A361868 #7 Apr 07 2023 09:24:26
%S A361868 12,20,24,28,40,42,44,48,52,56,60,63,66,68,72,76,78,80,84,88,92,96,99,
%T A361868 102,104,112,114,116,117,120,124,126,130,132,136,138,140,144,148,152,
%U A361868 153,156,160,164,168,170,171,172,174,176,184,186,188,189,190,192,195
%N A361868 Positive integers > 1 whose prime indices satisfy (maximum) >= 2*(median).
%C A361868 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A361868 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A361868 The prime indices of 84 are {1,1,2,4}, with maximum 4 and median 3/2, and 4 >= 2*(3/2), so 84 is in the sequence.
%e A361868 The terms together with their prime indices begin:
%e A361868    12: {1,1,2}
%e A361868    20: {1,1,3}
%e A361868    24: {1,1,1,2}
%e A361868    28: {1,1,4}
%e A361868    40: {1,1,1,3}
%e A361868    42: {1,2,4}
%e A361868    44: {1,1,5}
%e A361868    48: {1,1,1,1,2}
%e A361868    52: {1,1,6}
%e A361868    56: {1,1,1,4}
%e A361868    60: {1,1,2,3}
%e A361868    63: {2,2,4}
%e A361868    66: {1,2,5}
%e A361868    68: {1,1,7}
%e A361868    72: {1,1,1,2,2}
%t A361868 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A361868 Select[Range[100],Max@@prix[#]>=2*Median[prix[#]]&]
%Y A361868 The LHS is A061395 (greatest prime index).
%Y A361868 The RHS is A360005 (twice median), distinct A360457.
%Y A361868 The equal case is A361856, counted by A361849.
%Y A361868 These partitions are counted by A361859.
%Y A361868 The unequal case is A361867, counted by A361857.
%Y A361868 The complement is counted by A361858.
%Y A361868 A000975 counts subsets with integer median.
%Y A361868 A001222 (bigomega) counts prime factors, distinct A001221 (omega).
%Y A361868 A112798 lists prime indices, sum A056239.
%Y A361868 A325347 counts partitions with integer median, complement A307683.
%Y A361868 A359893 and A359901 count partitions by median.
%Y A361868 Cf. A027193, A053263, A111907, A118096, A237753, A237821, A361848, A361855, A361906, A361908.
%K A361868 nonn
%O A361868 1,1
%A A361868 _Gus Wiseman_, Apr 05 2023