A137230 -id:A137230 - cp's OEIS frontend

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

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

nonn

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

			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.

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

Cf. A001222, A074946, A137230.

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

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 }

A224705 Composite numbers n divisible by Omega(n)^2 (the square of the number of their prime factors, counted with multiplicity).

Original entry on oeis.org

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

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

nonn

A number n is in the sequence if and only if mod(n, A001222(n)^2) == 0 and n is not prime.

Without the restriction that n must be composite, all prime numbers would trivially be included in the sequence.

			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.

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

Cf. A001222, A074946, A137230, A070003, A224703.

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

Select[Range[2, 1000], ! PrimeQ[#] && Mod[#, PrimeOmega[#]^2] == 0 &] (* T. D. Noe, Apr 18 2013 *)

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 }

cp's OEIS Frontend

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

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