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%I #30 Sep 08 2022 08:44:37
%S 0,1,2097152,10460353203,4398046511104,476837158203125,
%T 21936950640377856,558545864083284007,9223372036854775808,
%U 109418989131512359209,1000000000000000000000,7400249944258160101211
%N 21st powers: a(n) = n^21.
%H Vincenzo Librandi, <a href="/A010809/b010809.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
%F Completely multiplicative sequence with a(p) = p^21 for prime p. Multiplicative sequence with a(p^e) = p^(21e). - _Jaroslav Krizek_, Nov 01 2009
%F From _Amiram Eldar_, Oct 09 2020: (Start)
%F Dirichlet g.f.: zeta(s-21).
%F Sum_{n>=1} 1/a(n) = zeta(21) (A293904).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1048575*zeta(21)/1048576. (End)
%t Table[n^21, {n, 0, 20}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010 *)
%o (Magma) [n^21: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o (PARI) a(n)=n^21 \\ _Felix Fröhlich_, Jul 16 2014
%Y Cf. A293904.
%K nonn,mult,easy
%O 0,3
%A _N. J. A. Sloane_.
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