A224703 Numbers divisible by the twice the number of their prime factors (counted with multiplicity), or numbers n divisible by 2*Omega(n).

2, 4, 12, 16, 18, 24, 30, 40, 42, 56, 66, 78, 80, 88, 96, 102, 104, 114, 120, 136, 138, 144, 152, 174, 180, 184, 186, 200, 216, 222, 232, 240, 246, 248, 256, 258, 270, 280, 282, 296, 300, 318, 324, 328, 336, 344, 354, 360, 366, 376, 384, 402, 420, 424, 426

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 16 2013

Keywords

• nonn

Comments

A number is in the list if mod(n,2*A001222(n)) == 0.

Examples

			18 has 3 prime factors {2,3,3} and is divisible by 6=2*3; 184 has 4 prime factors {2,2,2,23} and is divisible by 8=2*4.
		

Links

• Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A074946, A137230.

Programs

Mathematica

Select[Range[2, 426], Mod[#, 2*PrimeOmega[#]] == 0 &] (* T. D. Noe, Apr 17 2013 *)

R

y=c(); i=2; isint<-function(x) x==as.integer(x)
while(length(y)<10000) {if(isint(i/(2*length(factorize(i))))) y=c(y,i); i=i+1 }