A091703 Count, setting 5n to zero.

0, 1, 2, 3, 4, 0, 6, 7, 8, 9, 0, 11, 12, 13, 14, 0, 16, 17, 18, 19, 0, 21, 22, 23, 24, 0, 26, 27, 28, 29, 0, 31, 32, 33, 34, 0, 36, 37, 38, 39, 0, 41, 42, 43, 44, 0, 46, 47, 48, 49, 0, 51, 52, 53, 54, 0, 56, 57, 58, 59, 0, 61, 62, 63, 64, 0, 66, 67, 68, 69, 0, 71, 72, 73, 74, 0, 76, 77

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).

Formula

a(n) = Product_{k=0..4} Sum_{j=1..n} e^(2*Pi*ijk/5), i=sqrt(-1).

a(n) = cos(4*Pi*n/5 + 2*Pi/5)*(n*cos(2*Pi*n/5 + Pi/5)/5 + n*sqrt(1/5 - 2*sqrt(5)/25)*sin(2*Pi*n/5 + Pi/5) + n*(1/5 - sqrt(5)/5)) + sin(4*Pi*n/5 + 2*Pi/5)*(n*sqrt(2*sqrt(5)/25 + 1/5)*cos(2*Pi*n/5 + Pi/5) + sqrt(5)*n*sin(2*Pi*n/5 + Pi/5)/5 - n*sqrt(2*sqrt(5)/25 + 2/5)) - n*(sqrt(5)/5 + 1/5)*cos(2*Pi*n/5 + Pi/5) - n*sqrt(2/5 - 2*sqrt(5)/25)*sin(2*Pi*n/5 + Pi/5) + 4*n/5.

a(n) = n^5 mod (5*n). - Paul Barry, Apr 13 2005

Multiplicative with a(5^e) = 0, a(p^e) = p^e otherwise. - Mitch Harris, Jun 09 2005

From R. J. Mathar, Feb 04 2009: (Start)

a(n) = 2*a(n-5) - a(n-10).

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 4*x^5 + 3*x^6 + 2*x^7 + x^8)/(1-x^5)^2.

a(n) = |A080891(n)|*A001477(n). (End)

From R. J. Mathar, Apr 14 2011: (Start)

a(n) = n*A011558(n).

Dirichlet g.f.: (1-5^(1-s))*zeta(s-1). (End)

Sum_{k=1..n} a(k) ~ (2/5) * n^2. - Amiram Eldar, Nov 20 2022

Mathematica

Table[If[Divisible[n, 5], 0, n], {n, 0, 80}] (* Harvey P. Dale, Apr 26 2018 *)

Prog

(PARI) a(n) = if (n % 5, n, 0); \\ Michel Marcus, Feb 28 2019
(Magma) [(n mod 5 eq 0) select 0 else n: n in [0..80]]; // G. C. Greubel, Feb 28 2019
(Sage) [n if not n % 5==0 else 0 for n in range(80)] # G. C. Greubel, Feb 28 2019

Crossrefs

Cf. A001477, A011558, A080891, A091684, A011558.

Sequence in context: A129468 A236846 A236847 * A004180 A011418 A214158

Adjacent sequences: A091700 A091701 A091702 * A091704 A091705 A091706

Keyword

easy,nonn,mult

Author

Paul Barry, Jan 30 2004

Status

approved