A010801 - OEIS

%I #42 Sep 08 2022 08:44:37

%S 0,1,8192,1594323,67108864,1220703125,13060694016,96889010407,

%T 549755813888,2541865828329,10000000000000,34522712143931,

%U 106993205379072,302875106592253,793714773254144,1946195068359375,4503599627370496,9904578032905937,20822964865671168

%N 13th powers: a(n) = n^13.

%C a(n) mod 10 = n mod 10. - _Reinhard Zumkeller_, Dec 06 2004

%C Totally multiplicative sequence with a(p) = p^13 for primes p. Multiplicative sequence with a(p^e) = p^(13*e). - _Jaroslav Krizek_, Nov 01 2009

%H Vincenzo Librandi, <a href="/A010801/b010801.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

%F G.f.: x*(x^12 + 8178*x^11 + 1479726*x^10 + 45533450*x^9 + 423281535*x^8 + 1505621508*x^7 + 2275172004*x^6 + 1505621508*x^5 + 423281535*x^4 + 45533450*x^3 + 1479726*x^2 + 8178*x + 1) / (x - 1)^14. - _Colin Barker_, Sep 25 2014

%F From _Amiram Eldar_, Oct 08 2020: (Start)

%F Sum_{n>=1} 1/a(n) = zeta(13) (A013671).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 4095*zeta(13)/4096. (End)

%t Range[0,30]^13 (* _Vladimir Joseph Stephan Orlovsky_, Mar 14 2011 *)

%o (Magma) [n^13: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011

%o (PARI) a(n)=n^13 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A000290, A000578, A000583, A000584, A013671.

%K nonn,easy,mult

%O 0,3

%A _N. J. A. Sloane_