A030629 Numbers with 11 divisors.

1024, 59049, 9765625, 282475249, 25937424601, 137858491849, 2015993900449, 6131066257801, 41426511213649, 420707233300201, 819628286980801, 4808584372417849, 13422659310152401

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• easy

Comments

Let p be a prime. Then the n-th number with p divisors is equal to prime(n)^(p-1). - Omar E. Pol, May 06 2008

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• OEIS Wiki, Index entries for number of divisors

Crossrefs

Cf. A000005, A000040, A001248, A008454, A009087, A030514, A030516.

Cf. A013668, A013678.

Programs

Magma

[p^10: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

Mathematica

(Prime@Range@30)^10  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

PARI

is(n)=isprimepower(n)==10 \\ Charles R Greathouse IV, Jun 19 2016

Python

from sympy import prime
def A030629(n): return prime(n)**10 # Chai Wah Wu, Sep 13 2024

Sage

[p**10 for p in prime_range(100)]
# Zerinvary Lajos, May 16 2007

Formula

a(n) = A000040(n)^10, i.e. tenth power of n-th prime. - Henry Bottomley, Aug 20 2001

From Amiram Eldar, Jan 24 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(10)/zeta(20) = 16368226875/(174611*Pi^10) = A013668/A013678.

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(10) = 93555/Pi^10 = 1/A013668. (End)