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A361395
Positive integers k such that 2*omega(k) >= bigomega(k).
7
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, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74
OFFSET
1,2
COMMENTS
Differs from A068938 in having 1 and 4 and lacking 80.
Includes all squarefree numbers.
FORMULA
A001222(a(n)) <= 2*A001221(a(n)).
EXAMPLE
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.
MATHEMATICA
Select[Range[100], 2*PrimeNu[#]>=PrimeOmega[#]&]
CROSSREFS
Complement of A360558.
Positions of nonnegative terms in A361205.
These partitions are counted by A361394.
A001222 (bigomega) counts prime factors, distinct A001221 (omega).
A112798 lists prime indices, sum A056239.
A360005 gives median of prime indices (times 2), distinct A360457.
Comparing twice the number of distinct parts to the number of parts:
less: A360254, ranks A360558
equal: A239959, ranks A067801
greater: A237365, ranks A361393
less or equal: A237363, ranks A361204
greater or equal: A361394, ranks A361395
Sequence in context: A285316 A378287 A362147 * A329135 A182768 A368917
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 16 2023
STATUS
approved