A030516 Numbers with 7 divisors. 6th powers of primes.

64, 729, 15625, 117649, 1771561, 4826809, 24137569, 47045881, 148035889, 594823321, 887503681, 2565726409, 4750104241, 6321363049, 10779215329, 22164361129, 42180533641, 51520374361, 90458382169, 128100283921

Offset

1,1

Comments

These are the numbers p^6 with p prime. - Jorge Coveiro, Apr 13 2004

The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. - 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

Index to sequences related to prime signature

Formula

a(n) = A000040(n)^(7-1) = A000040(n)^6. - Omar E. Pol, May 06 2008

A056595(a(n)) = 3. - Reinhard Zumkeller, Aug 15 2011

Sum_{n>=1} 1/a(n) = P(6) = 0.0170700868... (A085966). - Amiram Eldar, Jul 27 2020

From Amiram Eldar, Jan 23 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(6)/zeta(12) = 675675/(691*Pi^6) (A269404).

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(6) = 945/Pi^6 = 1/A013664. (End)

Mathematica

Array[Prime[ # ]^6&, 60] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)

Prog

(Sage)
[p**6 for p in prime_range(100)]
# Zerinvary Lajos, May 16 2007
(PARI) for(n=1, 1e3, print1(prime(n)^6", "));  \\ Bruno Berselli, Jul 30 2011
(Magma) [NthPrime(n)^6: n in [1..400]];  // Bruno Berselli, Jul 30 2011
(Haskell)
a030516 = (^ 6) . a000040
a030516_list = map (^ 6) a000040_list
-- Reinhard Zumkeller, Jun 03 2015

Crossrefs

Subsequence of A046306.

Cf. A013664, A050997, A085966, A131993, A000005, A000040, A001248, A030514, A258603, A269404.

Sequence in context: A113851 A046455 A092758 * A056573 A321817 A231305

Adjacent sequences: A030513 A030514 A030515 * A030517 A030518 A030519

Keyword

nonn,easy

Author

Jeff Burch

Status

approved