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A030629
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Numbers with 11 divisors.
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32
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1024, 59049, 9765625, 282475249, 25937424601, 137858491849, 2015993900449, 6131066257801, 41426511213649, 420707233300201, 819628286980801, 4808584372417849, 13422659310152401
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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R. J. Mathar, Table of n, a(n) for n = 1..1000
OEIS Wiki, Index entries for number of divisors
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FORMULA
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a(n) = A000040(n)^10, i.e. tenth power of n-th prime. - Henry Bottomley, Aug 20 2001
From Amiram Eldar, Jan 24 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(10)/zeta(20) = 16368226875/(174611*Pi^10) = A013668/A013678.
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(10) = 93555/Pi^10 = 1/A013668. (End)
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MATHEMATICA
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(Prime@Range@30)^10 (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)
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PROG
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(Sage)
[p**10 for p in prime_range(100)]
# 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
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CROSSREFS
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Cf. A000005, A000040, A001248, A008454, A009087, A030514, A030516.
Cf. A013668, A013678.
Sequence in context: A016901 A017684 A008454 * A056587 A321819 A231309
Adjacent sequences: A030626 A030627 A030628 * A030630 A030631 A030632
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KEYWORD
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nonn,easy
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AUTHOR
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Jeff Burch
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STATUS
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approved
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