A323350 - OEIS

%I #12 Jan 15 2019 12:13:06

%S 16,24,36,40,54,56,60,81,84,88,90,100,104,126,132,135,136,140,150,152,

%T 156,184,189,196,198,204,210,220,225,228,232,234,248,250,260,276,294,

%U 296,297,306,308,315,328,330,340,342,344,348,350,351,364,372,375,376

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

%C First differs from A014613 in having 512.

%H Robert Israel, <a href="/A323350/b323350.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%e 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.

%e 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.

%p filter:= proc(n) local t;

%p   t:= numtheory:-bigomega(n);

%p   t > 1 and issqr(t)

%p end proc:

%p select(filter, [$4..1000]); # _Robert Israel_, Jan 15 2019

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

%o (PARI) isok(n) = (n>1) && !isprime(n) && issquare(bigomega(n)); \\ _Michel Marcus_, Jan 15 2019

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Jan 15 2019