login
A level 11 weight 5 form.
2

%I #16 Jan 19 2025 01:27:09

%S 1,15,82,241,626,1230,2400,3855,6643,9390,14641,19762,28560,36000,

%T 51332,61681,83520,99645,130320,150866,196800,219615,279842,316110,

%U 391251,428400,538084,578400,707280,769980,923522,986895,1200562

%N A level 11 weight 5 form.

%C Multiplicative because convolution of multiplicative functions. - _Michael Somos_, Jun 07, 2005

%H G. C. Greubel, <a href="/A065103/b065103.txt">Table of n, a(n) for n = 1..5000</a>

%H Ken Ono, <a href="https://doi.org/10.1006/jnth.1998.2354">On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function</a>, Journal of Number Theory, Volume 76, Issue 1, May 1999, Pages 62-65.

%F a(n) = Sum_{d | n} Kronecker(d/11)*(n/d)^4.

%t a[n_]:= If[n < 0, 0, Sum[KroneckerSymbol[d, 11]*(n/d)^4, {d, Divisors[n]}]]; Table[a[n], {n,1,50}] (* _G. C. Greubel_, Apr 17 2018 *)

%o (PARI) a(n) = sumdiv(n, d, kronecker(d, 11) * (n/d)^4); \\ _Amiram Eldar_, Jan 18 2025

%Y Cf. A011582.

%K nonn,mult

%O 1,2

%A Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Nov 20 2001