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A224705 Composite numbers n divisible by Omega(n)^2 (the square of the number of their prime factors, counted with multiplicity). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

EXAMPLE

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.

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

MATHEMATICA

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

PROG

(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 }

CROSSREFS

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

Sequence in context: A034121 A281685 A166620 * A243298 A139719 A117102

Adjacent sequences:  A224702 A224703 A224704 * A224706 A224707 A224708

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified October 25 03:54 EDT 2021. Contains 348237 sequences. (Running on oeis4.)