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%I #2 Mar 30 2012 17:36:44
%S 24,30,36,40,42,48,54,56,60,64,66,70,72,78,80,84,88,90,96,100,102,104,
%T 105,108,110,112,114,120,126,128,130,132,135,136,138,140,144,150,152,
%U 154,156,160,162,165,168,170,174,176,180,182,184,186,189,190,192,195
%N Numbers n that can be written as n = x*y*z with 1<x<y<z (A122180(n)>0).
%C Equivalently, numbers n with at least 7 divisors (A000005(n)>6). Equivalently, numbers n with at least 5 proper divisors (A070824(n)>4). Equivalently, numbers n such that i) n has at least three distinct prime factors (A000977), ii) n has two distinct prime factors and four or more total prime factors (n=p^j*q^k, p,q prime, j+k>=4), or iii) n=p^k, a perfect power (A001597) but restricted to prime p and k>=6 [=1+2+3] (some terms of A076470).
%e a(1) = 24 = 2*3*4, a product of three distinct proper divisors (omega(24)=2, bigomega(24)=4).
%e a(2) = 30 = 2*3*5, a product of three distinct prime factors (omega(30)=3).
%e a(10) = 64 = 2*4*8 [= 2^1*2^2*2^3] (omega(64)=1, bigomega(64)=6).
%o (PARI) for(n=1,300, if(numdiv(n)>6, print1(n,", ")) for(n=1,300, if( (omega(n)==1 && bigomega(n)>5) || (omega(n)==2 && bigomega(n)>3) || (omega(n)>2), print1(n,", ")))
%Y Cf. A122179, A122180, A000005, A070824, A000977, A001221, A001222, A001597, A076470.
%K nonn
%O 1,1
%A _Rick L. Shepherd_, Aug 24 2006
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