cp's OEIS Frontend

A361395 Positive integers k such that 2*omega(k) >= bigomega(k).

%I A361395 #6 Mar 16 2023 19:46:52
%S A361395 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 A361395 29,30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,
%U A361395 54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74
%N A361395 Positive integers k such that 2*omega(k) >= bigomega(k).
%C A361395 Differs from A068938 in having 1 and 4 and lacking 80.
%C A361395 Includes all squarefree numbers.
%F A361395 A001222(a(n)) <= 2*A001221(a(n)).
%e A361395 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 A361395 Select[Range[100],2*PrimeNu[#]>=PrimeOmega[#]&]
%Y A361395 Complement of A360558.
%Y A361395 Positions of nonnegative terms in A361205.
%Y A361395 These partitions are counted by A361394.
%Y A361395 A001222 (bigomega) counts prime factors, distinct A001221 (omega).
%Y A361395 A112798 lists prime indices, sum A056239.
%Y A361395 A360005 gives median of prime indices (times 2), distinct A360457.
%Y A361395 Comparing twice the number of distinct parts to the number of parts:
%Y A361395               less: A360254, ranks A360558
%Y A361395              equal: A239959, ranks A067801
%Y A361395            greater: A237365, ranks A361393
%Y A361395      less or equal: A237363, ranks A361204
%Y A361395   greater or equal: A361394, ranks A361395
%Y A361395 Cf. A046660, A061395, A067340, A111907.
%Y A361395 Cf. A324515, A324517, A324521, A324560, A324562.
%Y A361395 Cf. A360248, A360249, A360454.
%K A361395 nonn
%O A361395 1,2
%A A361395 _Gus Wiseman_, Mar 16 2023