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

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.

Links

Table of n, a(n) for n=1..67.

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

Cf. A046660, A061395, A067340, A111907.

Cf. A324515, A324517, A324521, A324560, A324562.

Cf. A360248, A360249, A360454.

Sequence in context: A068937 A285316 A362147 * A329135 A182768 A368917

Adjacent sequences: A361392 A361393 A361394 * A361396 A361397 A361398

Keyword

nonn

Author

Gus Wiseman, Mar 16 2023

Status

approved