A122970 -id:A122970 - cp's OEIS frontend

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

R. J. Mathar, Apr 22 2008

nonn

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

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

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

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

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

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

A000005(a(n))=30.

A122971 30th powers: a(n) = n^30.

Original entry on oeis.org

0, 1, 1073741824, 205891132094649, 1152921504606846976, 931322574615478515625, 221073919720733357899776, 22539340290692258087863249, 1237940039285380274899124224

Offset: 0

Franklin T. Adams-Watters, Oct 27 2006

Amiram Eldar, Table of n, a(n) for n = 0..10000

Cf. A122968, A122969, A122970.

Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers).

Range[0,10]^30 (* Harvey P. Dale, Mar 06 2019 *)

(A122971(n)=n^30); is_A122971(N)=ispower(N,30) \\ M. F. Hasler, Jul 24 2022

def A122971(n): return n**30
from sympy import nextprime
def is_A122971(N, k=30): # 2nd opt. arg to check for powers other than 30
    p = 2
    while N >= p**k:
        for e in range(N):
            if N % p: break
            N //= p
        if e % k: return False
        p = nextprime(p)
    return N < 2  #  M. F. Hasler, Jul 24 2022

Totally multiplicative sequence with a(p) = p^30 for prime p. Multiplicative sequence with a(p^e) = p^(30e). - Jaroslav Krizek, Nov 01 2009
From Amiram Eldar, Oct 09 2020: (Start)
Dirichlet g.f.: zeta(s-30).
Sum_{n>=1} 1/a(n) = zeta(30) = 6892673020804*Pi^30/5660878804669082674070015625.
Sum_{n>=1} (-1)^(n+1)/a(n) = 536870911*zeta(30)/536870912 = 925118910976041358111*Pi^30/759790291646040068357842010112000000. (End)
Intersection of A000290 and A000578 and A000584. - M. F. Hasler, Jul 24 2022

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A137493 Numbers with 30 divisors.

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A122971 30th powers: a(n) = n^30.

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