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A030516 Numbers with 7 divisors. 6th powers of primes. 63
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 (jorgecoveiro(AT)yahoo.com), 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

MATHEMATICA

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

PROG

(Sage) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^6) list # 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, A131993, A000005, A000040, A001248, A030514, A258603.

Sequence in context: A113851 A046455 A092758 * A056573 A231305 A108538

Adjacent sequences:  A030513 A030514 A030515 * A030517 A030518 A030519

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

STATUS

approved

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Last modified August 21 19:52 EDT 2017. Contains 290906 sequences.