A089081 - OEIS

%I #18 Sep 08 2022 08:45:12

%S 0,1,67108864,2541865828329,4503599627370496,1490116119384765625,

%T 170581728179578208256,9387480337647754305649,

%U 302231454903657293676544,6461081889226673298932241,100000000000000000000000000

%N 26th powers: a(n) = n^26.

%H Vincenzo Librandi, <a href="/A089081/b089081.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%F a(n) = n^26.

%F Completely multiplicative sequence with a(p) = p^26 for prime p. Multiplicative sequence with a(p^e) = p^(26e). - _Jaroslav Krizek_, Nov 01 2009

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

%F Dirichlet g.f.: zeta(s-26).

%F Sum_{n>=1} 1/a(n) = zeta(26) = 1315862*Pi^26/11094481976030578125.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 33554431*zeta(26)/33554432 = 22076500342261*Pi^26/186134520519971831808000000. (End)

%t Range[0, 9]^26 (* _Alonso del Arte_, Apr 26 2015 *)

%o (Magma) [n^26: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%o (PARI) a(n)=n^26 \\ _Charles R Greathouse IV_, Jun 28 2015

%Y Cf. A008454-A008456, A010801-A010813.

%K nonn,mult,easy

%O 0,3

%A Douglas Winston (douglas.winston(AT)srupc.com), Dec 04 2003