cp's OEIS Frontend

A010801 13th powers: a(n) = n^13.

%I A010801 #45 Jul 05 2025 16:07:19
%S A010801 0,1,8192,1594323,67108864,1220703125,13060694016,96889010407,
%T A010801 549755813888,2541865828329,10000000000000,34522712143931,
%U A010801 106993205379072,302875106592253,793714773254144,1946195068359375,4503599627370496,9904578032905937,20822964865671168
%N A010801 13th powers: a(n) = n^13.
%H A010801 Vincenzo Librandi, <a href="/A010801/b010801.txt">Table of n, a(n) for n = 0..1000</a>
%H A010801 <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 A010801 a(n) mod 10 = n mod 10. - _Reinhard Zumkeller_, Dec 06 2004
%F A010801 Totally multiplicative with a(p) = p^13 for primes p. Multiplicative with a(p^e) = p^(13*e). - _Jaroslav Krizek_, Nov 01 2009
%F A010801 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 A010801 From _Amiram Eldar_, Oct 08 2020: (Start)
%F A010801 Sum_{n>=1} 1/a(n) = zeta(13) (A013671).
%F A010801 Sum_{n>=1} (-1)^(n+1)/a(n) = 4095*zeta(13)/4096. (End)
%p A010801 A010801 := n -> n^13; \\ _M. F. Hasler_, Jul 03 2025
%t A010801 Range[0,30]^13 (* _Vladimir Joseph Stephan Orlovsky_, Mar 14 2011 *)
%o A010801 (Magma) [n^13: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o A010801 (PARI) A010801(n)=n^13 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A010801 (Python) A010801 = lambda n: n**13 # _M. F. Hasler_, Jul 03 2025
%Y A010801 Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A000584 (5th powers), A008455 (11th powers), A013671 (zeta(11)).
%K A010801 nonn,easy,mult
%O A010801 0,3
%A A010801 _N. J. A. Sloane_