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A030631 Numbers with 13 divisors. 27
4096, 531441, 244140625, 13841287201, 3138428376721, 23298085122481, 582622237229761, 2213314919066161, 21914624432020321, 353814783205469041, 787662783788549761, 6582952005840035281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

12th powers of primes. 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'=12*n^(11/12), 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

FORMULA

a(n)=A000040(n)^(13-1)=A000040(n)^(12). - Omar E. Pol, May 06 2008

MATHEMATICA

(Prime@Range@30)^12  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

PROG

(MAGMA) [p^12: p in PrimesUpTo(100)]; // Vincenzo Librandi, Mar 27 2014

(PARI) is(n)=isprimepower(n)==12 \\ Charles R Greathouse IV, Jun 19 2016

CROSSREFS

Cf. A000040, A030629.

Subsequence of A008456.

Sequence in context: A016902 A017688 A008456 * A236218 A016962 A224395

Adjacent sequences:  A030628 A030629 A030630 * A030632 A030633 A030634

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

STATUS

approved

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Last modified October 22 02:06 EDT 2017. Contains 293756 sequences.