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%I #6 Mar 16 2023 19:46:52
%S 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,28,
%T 29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,
%U 54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74
%N Positive integers k such that 2*omega(k) >= bigomega(k).
%C Differs from A068938 in having 1 and 4 and lacking 80.
%C Includes all squarefree numbers.
%F A001222(a(n)) <= 2*A001221(a(n)).
%e The prime indices of 80 are {1,1,1,1,3}, with 5 parts and 2 distinct parts, and 2*2 < 5, so 80 is not in the sequence.
%t Select[Range[100],2*PrimeNu[#]>=PrimeOmega[#]&]
%Y Complement of A360558.
%Y Positions of nonnegative terms in A361205.
%Y These partitions are counted by A361394.
%Y A001222 (bigomega) counts prime factors, distinct A001221 (omega).
%Y A112798 lists prime indices, sum A056239.
%Y A360005 gives median of prime indices (times 2), distinct A360457.
%Y Comparing twice the number of distinct parts to the number of parts:
%Y less: A360254, ranks A360558
%Y equal: A239959, ranks A067801
%Y greater: A237365, ranks A361393
%Y less or equal: A237363, ranks A361204
%Y greater or equal: A361394, ranks A361395
%Y Cf. A046660, A061395, A067340, A111907.
%Y Cf. A324515, A324517, A324521, A324560, A324562.
%Y Cf. A360248, A360249, A360454.
%K nonn
%O 1,2
%A _Gus Wiseman_, Mar 16 2023
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