A224705 Composite numbers n divisible by Omega(n)^2 (the square of the number of their prime factors, counted with multiplicity).
4, 16, 18, 27, 45, 63, 99, 117, 144, 153, 171, 200, 207, 216, 256, 261, 279, 300, 324, 333, 360, 369, 384, 387, 423, 450, 477, 500, 504, 531, 540, 549, 576, 603, 639, 640, 657, 675, 700, 711, 747, 750, 756, 792, 801, 873, 896, 900, 909, 927, 936, 960, 963, 981
Offset: 1
Keywords
Examples
a(6)=63=3*3*7, and 63 is divisible by 9=3^2; a(9)=144, which has 6 prime factors and is divisible by 36.
Links
- Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Programs
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Maple
isA224705 := proc(n) if isprime(n) then return false; else if modp(n,numtheory[bigomega](n)^2) = 0 then true; else false; end if; end if; end proc: n := 1; c := 4; while n <= 10000 do if isA224705(c) then printf("%d %d\n",n,c) ; n := n+1 ; end if; c := c+1 ; end do: # R. J. Mathar, Mar 14 2016
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Mathematica
Select[Range[2, 1000], ! PrimeQ[#] && Mod[#, PrimeOmega[#]^2] == 0 &] (* T. D. Noe, Apr 18 2013 *)
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R
y=c(); i=2; isint<-function(x) x==as.integer(x) while(length(y)<10000) {Omega=length(factorize(i)); if(Omega>1) if(isint(i/Omega^2)) y=c(y,i); i=i+1 }
Comments