cp's OEIS Frontend

A361867 Positive integers > 1 whose prime indices satisfy (maximum) > 2*(median).

%I A361867 #6 Apr 06 2023 21:44:06
%S A361867 20,28,40,44,52,56,66,68,76,78,80,84,88,92,99,102,104,112,114,116,117,
%T A361867 120,124,132,136,138,148,152,153,156,160,164,168,170,171,172,174,176,
%U A361867 184,186,188,190,198,200,204,207,208,212,220,222,224,228,230,232,234
%N A361867 Positive integers > 1 whose prime indices satisfy (maximum) > 2*(median).
%C A361867 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 A361867 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 A361867 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 A361867 The terms together with their prime indices begin:
%e A361867    20: {1,1,3}
%e A361867    28: {1,1,4}
%e A361867    40: {1,1,1,3}
%e A361867    44: {1,1,5}
%e A361867    52: {1,1,6}
%e A361867    56: {1,1,1,4}
%e A361867    66: {1,2,5}
%e A361867    68: {1,1,7}
%e A361867    76: {1,1,8}
%e A361867    78: {1,2,6}
%e A361867    80: {1,1,1,1,3}
%e A361867    84: {1,1,2,4}
%e A361867    88: {1,1,1,5}
%e A361867    92: {1,1,9}
%e A361867    99: {2,2,5}
%t A361867 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A361867 Select[Range[100], Max@@prix[#]>2*Median[prix[#]]&]
%Y A361867 The LHS is A061395 (greatest prime index).
%Y A361867 The RHS is A360005 (twice median), distinct A360457.
%Y A361867 The equal version is A361856, counted by A361849.
%Y A361867 These partitions are counted by A361857, reverse A361858.
%Y A361867 Including the equal case gives A361868, counted by A361859.
%Y A361867 For mean instead of median we have A361907.
%Y A361867 A000975 counts subsets with integer median.
%Y A361867 A001222 counts prime factors, distinct A001221.
%Y A361867 A112798 lists prime indices, sum A056239.
%Y A361867 Cf. A053263, A067801, A111907, A237751, A237820, A359893, A361848, A361855, A361908, A361909.
%K A361867 nonn
%O A361867 1,1
%A A361867 _Gus Wiseman_, Apr 05 2023