A137493 - OEIS

%I #21 Nov 18 2021 13:40:40

%S 720,1008,1200,1584,1620,1872,2268,2352,2448,2592,2736,2800,3312,3564,

%T 3888,3920,4050,4176,4212,4400,4464,4608,5200,5328,5508,5808,5904,

%U 6156,6192,6768,6800,7452,7500,7600,7632,7938,8112,8496,8624,8784,9200,9396

%N Numbers with 30 divisors.

%C Maple implementation: see A030513.

%C 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 T. D. Noe, <a href="/A137493/b137493.txt">Table of n, a(n) for n = 1..1000</a>

%F A000005(a(n))=30.

%t Select[Range[10000],DivisorSigma[0,#]==30&]  (* _Harvey P. Dale_, Feb 18 2011 *)

%o (PARI) is(n)=numdiv(n)==30 \\ _Charles R Greathouse IV_, Jun 19 2016

%o (PARI) list(lim)=

%o {

%o   my(f=(v,s)->concat(v,listsig(lim,s,1)));

%o   Set(fold(f, [[], [29], [5, 4], [9, 2], [14, 1], [4, 2, 1]]));

%o }

%o listsig(lim, sig, coprime)=

%o {

%o   my(e=sig[1]);

%o   if(#sig<2,

%o     if(#sig==0 || sig[1]==0, return(if(lim<1,[],[1])));

%o     my(P=primes([2,sqrtnint(lim\1,e)]));

%o     if(coprime==1, return(if(e>1,apply(p->p^e,P),P)));

%o     P=select(p->gcd(p,coprime)==1, P);

%o     if(e>1, P=apply(p->p^e, P));

%o     return(P);

%o   );

%o   my(v=List(),ss=sig[2..#sig],t=leastOfSig(ss));

%o   forprime(p=2,sqrtnint(lim\t,e),

%o     if(coprime%p,

%o         my(u=listsig(lim\p^e,ss,coprime*p));

%o         for(i=1,#u, listput(v,p^e*u[i]));

%o     )

%o   );

%o   Vec(v);

%o } \\ _Charles R Greathouse IV_, Nov 18 2021

%Y Cf. A137492 (29 divs), A139571 (31 divs).

%K nonn

%O 1,1

%A _R. J. Mathar_, Apr 22 2008