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

1,1

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

Formula

A000005(a(n))=30.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A067892 A337036 A257416 * A179669 A067808 A302127

Adjacent sequences: A137490 A137491 A137492 * A137494 A137495 A137496

Keyword

nonn

Author

R. J. Mathar, Apr 22 2008

Status

approved