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A245080 Numbers such that omega(a(n)) is a proper divisor of bigomega(a(n)). 2

%I

%S 4,8,9,16,24,25,27,32,36,40,49,54,56,64,81,88,96,100,104,121,125,128,

%T 135,136,144,152,160,169,184,189,196,216,224,225,232,240,243,248,250,

%U 256,289,296,297,324,328,336,343,344,351,352,360,361,375,376,384,400,416,424,441,459

%N Numbers such that omega(a(n)) is a proper divisor of bigomega(a(n)).

%C All proper powers of any number greater than 1 (A001597(n), n>1) are a subset of this sequence. On the other hand, this is a subset of A067340 which admits also numbers k for which bigomega(k) = omega(k). In particular, prime numbers are excluded.

%C The density of these numbers, i.e., the ratio n/a(n), apparently decreases with n, reaching 0.04420... for n = 10000000. Conjecture: n/a(n) might have a nonzero limit below 0.0427 (the density found in the interval 9500000 < n <= 10000000).

%H Stanislav Sykora, <a href="/A245080/b245080.txt">Table of n, a(n) for n = 1..20000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_functions">Arithmetic functions</a>

%e 240 is in the sequence because 240=5^1*3^1*2^4. Hence omega(240)=3 (three distinct prime divisors) is a proper divisor of bigomega(240)=6 (six prime divisors with multiplicity).

%o (PARI) OmegaTest(n)=(bigomega(n)>omega(n))&&(bigomega(n)%omega(n)==0);

%o Ntest(nmax,test)={my(k=1,n=0,v);v=vector(nmax);while(1,n++;if(test(n),v[k]=n;k++;if(k>nmax,break)););return(v);}

%o Ntest(20000,OmegaTest)

%Y Cf. A000040, A001597, A067340, A070011.

%K nonn

%O 1,1

%A _Stanislav Sykora_, Jul 11 2014

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Last modified January 17 22:51 EST 2019. Contains 319251 sequences. (Running on oeis4.)