A360668 Numbers > 1 whose greatest prime index is not divisible by their number of prime factors (bigomega).

4, 8, 10, 12, 15, 16, 18, 22, 24, 25, 27, 28, 32, 33, 34, 36, 40, 42, 44, 46, 48, 51, 54, 55, 60, 62, 63, 64, 66, 68, 69, 70, 72, 76, 77, 80, 81, 82, 85, 88, 90, 93, 94, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 115, 116, 118, 119, 120, 121, 123, 124

Offset

1,1

Comments

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.

Also numbers > 1 whose first differences of 0-prepended prime indices have non-integer mean.

Links

Table of n, a(n) for n=1..62.

Example

The prime indices of 1617 are {2,4,4,5}, and 5 is not divisible by 4, so 1617 is in the sequence.

Mathematica

Select[Range[2, 100], !Divisible[PrimePi[FactorInteger[#][[-1, 1]]], PrimeOmega[#]]&]

Crossrefs

These partitions are counted by A200727.

The complement is A340610 (without 1), counted by A168659.

For median instead of mean we have A360557, counted by A360691.

Positions of terms > 1 in A360615 (numerator: A360614).

A058398 counts partitions by mean, see also A008284, A327482.

A067340 lists numbers whose prime signature has integer mean.

A112798 = prime indices, length A001222, sum A056239, mean A326567/A326568.

A334201 adds up all prime indices except the greatest.

A348551 = numbers w/ non-integer mean of prime indices, complement A316413.

Cf. A072978, A078175, A139710, A307683, A359912, A360551, A360554, A360556, A360669.

Sequence in context: A358228 A230854 A377035 * A038801 A310977 A354526

Adjacent sequences: A360665 A360666 A360667 * A360669 A360670 A360671

Keyword

nonn

Author

Gus Wiseman, Feb 17 2023

Status

approved