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

Author

Gus Wiseman, Jan 15 2019

Keywords

• nonn

Comments

First differs from A014613 in having 512.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

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