

A030516


Numbers with 7 divisors. 6th powers of primes.


73



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

1,1


COMMENTS

These are the numbers p^6 with p prime.  Jorge Coveiro, Apr 13 2004
The nth number with p divisors is equal to the nth prime raised to power p1, where p is prime.  Omar E. Pol, May 06 2008
Solutions of the equation n'=6*n^(5/6), where n' is the arithmetic derivative of n.  Paolo P. Lava, Oct 31 2012


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)^(71)=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


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. A050997, A085966, A131993, A000005, A000040, A001248, A030514, A258603.
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



