A352550 - OEIS

%I #28 Nov 24 2023 21:17:00

%S 1,0,0,1,1,0,0,0,1,0,2,0,0,0,0,2,0,0,2,1,0,0,0,0,2,0,0,0,2,0,2,0,0,0,

%T 0,1,0,0,0,0,2,0,0,2,1,0,0,0,1,0,0,0,0,0,2,0,0,0,2,0,2,0,0,3,0,0,0,0,

%U 0,0,2,0,0,0,0,2,0,0,2,2,2,0,0,0,0,0,0,0,2,0,0,0,0,0,2

%N a(n) = number of modules with n elements over the ring of integers in the real quadratic field of discriminant 5.

%H Don Zagier, <a href="/A352550/a352550.txt">On the Number of n-Element Modules Over the Ring of Integers in a Quadratic Number Field</a> [Based on email to N. J. A. Sloane, March 18 2022]

%o (PARI) \\ Don Zagier, Mar 18 2022

%o PZ(D,m=20) = Z=dirmul(vector(m,n,1),vD=vector(m,n,kronecker(D,n))); v=Z; \

%o for(j=2,log(m)/log(2), V=v*0;for(k=1,m^(1/j),V[k^j]=Z[k]);v=dirmul(v,V)); v

%o PZ(5,100)

%Y Cf. A038540, A038541, A248107, A352551-A352567.

%K nonn

%O 1,11

%A _N. J. A. Sloane_, Mar 20 2022