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

Author

Gus Wiseman, Feb 17 2023

Keywords

• nonn

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.

Examples

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

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.

Programs

Mathematica

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