login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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)^(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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 01:48 EST 2020. Contains 338864 sequences. (Running on oeis4.)