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A030629 Numbers with 11 divisors. 27
1024, 59049, 9765625, 282475249, 25937424601, 137858491849, 2015993900449, 6131066257801, 41426511213649, 420707233300201, 819628286980801, 4808584372417849, 13422659310152401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let p be a prime. Then the n-th number with p divisors is equal to prime(n)^(p-1). - Omar E. Pol, May 06 2008

Solutions of the equation n'=10*n^(9/10), 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

FORMULA

a(n) =A000040(n)^10, i.e. tenth power of n-th prime. - Henry Bottomley, Aug 20 2001

MATHEMATICA

(Prime@Range@30)^10  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

PROG

(Sage) BB = primes_first_n(36) list = [] for i in range(36): list.append(BB[i]^10) list # Zerinvary Lajos, May 16 2007

(MAGMA) [p^10: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

(PARI) is(n)=isprimepower(n)==10 \\ Charles R Greathouse IV, Jun 19 2016

CROSSREFS

Cf. A000005, A000040, A001248, A008454, A009087, A030514, A030516.

Sequence in context: A016901 A017684 A008454 * A056587 A231309 A134847

Adjacent sequences:  A030626 A030627 A030628 * A030630 A030631 A030632

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

STATUS

approved

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Last modified August 20 11:41 EDT 2017. Contains 290835 sequences.