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A137493 Numbers with 30 divisors. 8
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 22 2008
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)