A197082 - OEIS

%I #24 Mar 30 2012 17:35:25

%S 2,9,75,625,5145,42875,352947,2941225,28824005,282475249,4882786447,

%T 60287465315,744365643175,10212696624361,118890080527911,

%U 1387050939492295,17125833028425275,211451611881577375,2584630720649942503,30088718564300934153,351035049916844231785

%N Smallest number with n prime divisors (counted with multiplicity) which is not divisible by a(k) for any k < n.

%C Conjecture: every proper divisor of a member of this sequence divides infinitely many numbers in the sequence.

%e For a(3), there must be 3 prime divisors. 2 cannot be a divisor, and there can be at most one 3 (otherwise a(1) or a(2) would divide it). The smallest product of three primes subject to these constraints is 3*5*5 = 75.

%o (PARI)oddfactfollow(n)={local(fm,np,r);

%o   fm=factor(n);np=matsize(fm)[1];r=[];

%o   if(fm[1,1]==3,r=concat(r,[n\3*5]);

%o     if(np>1&&fm[2,2]==1&&primepi(fm[2,1])<=lim,

%o       r=concat(r,[n\fm[2,1]*nextprime(fm[2,1]+1)])),

%o     if(fm[1,2]==1&&primepi(fm[1,1])<=lim,

%o       r=concat(r,[n\fm[1,1]*nextprime(fm[1,1]+1)])));r}

%o anydiv(v,n,x)=for(k=1,n,if(x%v[k]==0,return(1)));0

%o al(n) = {local(r,ms);r=vector(n);r[1]=2;

%o   for(k=2,n,ms=[3^k];

%o     while(anydiv(r,k-1,ms[1]),

%o       ms=vecsort(concat(vector(#ms-1,j,ms[j+1]),oddfactfollow(ms[1]))))

%o     r[k]=ms[1]);

%o   r}

%Y Cf. A001222.

%K nonn

%O 1,1

%A _Franklin T. Adams-Watters_, Oct 19 2011

%E More terms from _D. S. McNeil_, Oct 19 2011