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A010810 22nd powers: a(n) = n^22. 5

%I #24 Sep 08 2022 08:44:37

%S 0,1,4194304,31381059609,17592186044416,2384185791015625,

%T 131621703842267136,3909821048582988049,73786976294838206464,

%U 984770902183611232881,10000000000000000000000,81402749386839761113321

%N 22nd powers: a(n) = n^22.

%H Vincenzo Librandi, <a href="/A010810/b010810.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (23, -253, 1771, -8855, 33649, -100947, 245157, -490314, 817190, -1144066, 1352078, -1352078, 1144066, -817190, 490314, -245157, 100947, -33649, 8855, -1771, 253, -23, 1).

%F Totally multiplicative sequence with a(p) = p^22 for prime p. Multiplicative sequence with a(p^e) = p^(22e). - _Jaroslav Krizek_, Nov 01 2009

%F From _Amiram Eldar_, Oct 09 2020: (Start)

%F Dirichlet g.f.: zeta(s-22).

%F Sum_{n>=1} 1/a(n) = zeta(22) = 155366*Pi^22/13447856940643125.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2097151*zeta(22)/2097152 = 3324754717*Pi^22/287777551824322560000. (End)

%t Table[n^20, {n, 0, 22}] (* _Amiram Eldar_, Oct 09 2020 *)

%o (Magma) [n^22: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%o (PARI) a(n) = n^22; \\ _Michel Marcus_, Feb 27 2018

%Y Cf. A010807, A013678, A010809.

%K nonn,mult,easy

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)