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A137493 Numbers with 30 divisors.

%I A137493 #21 Nov 18 2021 13:40:40
%S A137493 720,1008,1200,1584,1620,1872,2268,2352,2448,2592,2736,2800,3312,3564,
%T A137493 3888,3920,4050,4176,4212,4400,4464,4608,5200,5328,5508,5808,5904,
%U A137493 6156,6192,6768,6800,7452,7500,7600,7632,7938,8112,8496,8624,8784,9200,9396
%N A137493 Numbers with 30 divisors.
%C A137493 Maple implementation: see A030513.
%C A137493 Numbers of the form p^29 (subset of A122970), p*q^2*r^4 (A179669), p^4*q^5 (A179702), p^2*q^9 (like 4608) or p*q^14, where p, q and r are distinct primes. - _R. J. Mathar_, Mar 01 2010
%H A137493 T. D. Noe, <a href="/A137493/b137493.txt">Table of n, a(n) for n = 1..1000</a>
%F A137493 A000005(a(n))=30.
%t A137493 Select[Range[10000],DivisorSigma[0,#]==30&]  (* _Harvey P. Dale_, Feb 18 2011 *)
%o A137493 (PARI) is(n)=numdiv(n)==30 \\ _Charles R Greathouse IV_, Jun 19 2016
%o A137493 (PARI) list(lim)=
%o A137493 {
%o A137493   my(f=(v,s)->concat(v,listsig(lim,s,1)));
%o A137493   Set(fold(f, [[], [29], [5, 4], [9, 2], [14, 1], [4, 2, 1]]));
%o A137493 }
%o A137493 listsig(lim, sig, coprime)=
%o A137493 {
%o A137493   my(e=sig[1]);
%o A137493   if(#sig<2,
%o A137493     if(#sig==0 || sig[1]==0, return(if(lim<1,[],[1])));
%o A137493     my(P=primes([2,sqrtnint(lim\1,e)]));
%o A137493     if(coprime==1, return(if(e>1,apply(p->p^e,P),P)));
%o A137493     P=select(p->gcd(p,coprime)==1, P);
%o A137493     if(e>1, P=apply(p->p^e, P));
%o A137493     return(P);
%o A137493   );
%o A137493   my(v=List(),ss=sig[2..#sig],t=leastOfSig(ss));
%o A137493   forprime(p=2,sqrtnint(lim\t,e),
%o A137493     if(coprime%p,
%o A137493         my(u=listsig(lim\p^e,ss,coprime*p));
%o A137493         for(i=1,#u, listput(v,p^e*u[i]));
%o A137493     )
%o A137493   );
%o A137493   Vec(v);
%o A137493 } \\ _Charles R Greathouse IV_, Nov 18 2021
%Y A137493 Cf. A137492 (29 divs), A139571 (31 divs).
%K A137493 nonn
%O A137493 1,1
%A A137493 _R. J. Mathar_, Apr 22 2008