A063989 -id:A063989 - cp's OEIS frontend

A323350 Nonprime numbers > 1 whose number of prime factors counted with multiplicity is a perfect square.

16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376

Offset: 1

Gus Wiseman, Jan 15 2019

nonn

First differs from A014613 in having 512.

			360 = 2*2*2*3*3*5 has 6 prime factors, and 6 is not a perfect square, so 360 does not belong to the sequence.
2160 = 2*2*2*2*3*3*3*5 has 8 prime factors, and 8 is not a perfect square, so 2160 does not belong to the sequence.
10800 = 2*2*2*2*3*3*3*5*5 has 9 prime factors, and 9 is a perfect square, so 10800 belongs to the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A001222, A063989, A067028, A067340, A070175, A071625, A118914, A167175, A323305.

filter:= proc(n) local t;
  t:= numtheory:-bigomega(n);
  t > 1 and issqr(t)
end proc:
select(filter, [$4..1000]); # Robert Israel, Jan 15 2019

Select[Range[100],#>1&&!PrimeQ[#]&&IntegerQ[Sqrt[PrimeOmega[#]]]&]

isok(n) = (n>1) && !isprime(n) && issquare(bigomega(n)); \\ Michel Marcus, Jan 15 2019

A114987 Numbers with a 3-almost prime number of prime divisors (counted with multiplicity).

Original entry on oeis.org

256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4096, 4160, 4374, 4416, 4536, 4704

Offset: 1

Jonathan Vos Post, Feb 22 2006

This is the 3-almost prime analog of A063989 "numbers with a prime number of prime divisors (counted with multiplicity)" and A110893 "numbers with a semiprime number of prime divisors (counted with multiplicity)." Below 4096, this is identical to 8-almost primes (A014613). Between 4096 and 6144, this is identical to 8-almost primes. Below 262144 this is identical to the union of 8-almost primes (A014613) and 12-almost primes (A069273). Between 262144 and 393216, this is identical to the union of 8-almost primes and 12-almost primes.

			a(1) = 256 because 256 = 2^8, which has a 3-almost prime (8) number of prime factors with multiplicity.
a(38) = 4096 because 4096 = 2^12, which has a 3-almost prime (12) number of prime factors with multiplicity.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001222, A014612, A014613, A069273, A069279, A069281.

Select[Range[5000],PrimeOmega[PrimeOmega[#]]==3&] (* Harvey P. Dale, Apr 12 2015 *)

is(n)=bigomega(bigomega(n))==3 \\ Charles R Greathouse IV, Feb 05 2017

a(n) such that A001222(A001222(a(n))) = 3. a(n) such that A001222(a(n)) is an element of A014612. a(n) such that bigomega(a(n)) is an element of A014612. Union[8-almost primes (A014613), 12-almost primes (A069273), 18-almost primes (A069279), 20-almost primes (A069281), 27-almost primes]...

cp's OEIS Frontend

A323350 Nonprime numbers > 1 whose number of prime factors counted with multiplicity is a perfect square.

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