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A030631
Numbers with 13 divisors.
30
4096, 531441, 244140625, 13841287201, 3138428376721, 23298085122481, 582622237229761, 2213314919066161, 21914624432020321, 353814783205469041, 787662783788549761, 6582952005840035281, 22563490300366186081, 39959630797262576401, 116191483108948578241
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
LINKS
FORMULA
a(n) = A000040(n)^(13-1) = A000040(n)^(12). - Omar E. Pol, May 06 2008
From Amiram Eldar, Jan 24 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = zeta(12)/zeta(24) = 218517792968475/(236364091*Pi^12).
Product_{n>=1} (1 - 1/a(n)) = 1/zeta(12) = 638512875/(691*Pi^12) = 1/A013670. (End)
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
Subsequence of A008456.
Sequence in context: A016902 A017688 A008456 * A321820 A236218 A016962
KEYWORD
nonn,easy
AUTHOR
STATUS
approved