A137493 Numbers with 30 divisors.

720, 1008, 1200, 1584, 1620, 1872, 2268, 2352, 2448, 2592, 2736, 2800, 3312, 3564, 3888, 3920, 4050, 4176, 4212, 4400, 4464, 4608, 5200, 5328, 5508, 5808, 5904, 6156, 6192, 6768, 6800, 7452, 7500, 7600, 7632, 7938, 8112, 8496, 8624, 8784, 9200, 9396

Offset: 1

Author

R. J. Mathar, Apr 22 2008

Keywords

• nonn

Comments

Maple implementation: see A030513.

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

Select[Range[10000],DivisorSigma[0,#]==30&]  (* Harvey P. Dale, Feb 18 2011 *)

PARI

is(n)=numdiv(n)==30 \\ Charles R Greathouse IV, Jun 19 2016

PARI

list(lim)=
{
  my(f=(v,s)->concat(v,listsig(lim,s,1)));
  Set(fold(f, [[], [29], [5, 4], [9, 2], [14, 1], [4, 2, 1]]));
}
listsig(lim, sig, coprime)=
{
  my(e=sig[1]);
  if(#sig<2,
    if(#sig==0 || sig[1]==0, return(if(lim<1,[],[1])));
    my(P=primes([2,sqrtnint(lim\1,e)]));
    if(coprime==1, return(if(e>1,apply(p->p^e,P),P)));
    P=select(p->gcd(p,coprime)==1, P);
    if(e>1, P=apply(p->p^e, P));
    return(P);
  );
  my(v=List(),ss=sig[2..#sig],t=leastOfSig(ss));
  forprime(p=2,sqrtnint(lim\t,e),
    if(coprime%p,
        my(u=listsig(lim\p^e,ss,coprime*p));
        for(i=1,#u, listput(v,p^e*u[i]));
    )
  );
  Vec(v);
} \\ Charles R Greathouse IV, Nov 18 2021

Formula

A000005(a(n))=30.